Miscellaneous

Are y = 3x + 4 and 6x - 2y = 10 parallel?

Which form is most useful for identifying the y-intercept at a glance?

Identify form: \(y = 10.\)

Perpendicular lines meet at a 90-degree angle. Their slopes are 'negative reciprocals,' meaning if one slope is a/b, the other is

If a line has a positive x-intercept and a positive y-intercept, which direction must the slope be?

In solving x + 7 = -3, a student gets x = 4. What did they do wrong?

If I walk at 5 mph instead of 4 mph, I save 15 minutes. How far am I walking?

Solve for x: \(2(x + 4) = 18\)

Slope of a line perpendicular to y = x.

Convert y = -x + 6 to Standard Form.

Solve for w: \(P = 2l + 2w\)

If m(x - 2) = 4x + 1 has no solution, what is m?

Perpendicular slope to m = -2/3.

Solve for C: \(F = (9/5)C + 32\)

Solve: \(2/x + 3/x = 1\)

What is the slope of the line represented by the equation 5x + 2y = 10?

Solve for h: \(V = (1/3)πr²h\)

A number's 3/4 part is 10 more than its 1/2 part. Find the number.

For what value of 'a' and 'b' does ax + 7 = 3x + b have infinite solutions?

Which equation is in slope-intercept form?

Two angles of a triangle are equal. The third is 30° more than the others. Find the equal angles.

Calculate the y-intercept for the line 0.5x + 0.1y = 1.

Solve for x in terms of a and b: \(a(x - b) = b(x + a)\)

On a graph, Line 1 rises 3 units for every 2 units it moves right. Line 2 also rises 3 units for every 2 units it moves right. These lines are

Convert 3x - 3y = 9 to slope-intercept form.

If the side of a square is doubled, the perimeter increases by 20 units. What was the original side?

From the equation y - 5 = -3(x + 2), which specific point is the line known to pass through?

Solve: \(3 / x = 12 / (x + 3)\)

Is y = 5 parallel to y = -5?

One number is 5 more than twice another. Their sum is 20. Find the smaller number.

Find the slope of -2x + 8y = 16.

If a line passes through the origin (0, 0), what are its intercepts?

A line with a slope of 0 (horizontal) is always perpendicular to a line with what kind of slope?

Which type of line is parallel to the horizontal line y = 10?

Solve: \(3x + 4 = 3x - 2\)

Solve: \(|3x - 5| = |3x + 5|\)

What is the y-intercept of y + 2 = 3(x - 1)?

What is the x-intercept of the line x + y = 0?

Solve for a: \(F = ma\)

Write the Standard Form of a line where m = 2 and the y-intercept is 3.

Solve: \(|3x + 2| = 11\)

X-intercept of 3x + y = 9?

What is the slope of the x-axis?

To convert 3x + y = 10 into slope-intercept form, what is the first algebraic step?

If you have y - 4 = 2(x - 3), what is the resulting equation in slope-intercept form after simplifying?

Slope of a line through the origin and (2, 4)?

Which line is parallel to x = 0 (the y-axis)?

A student says y = 2x + 5 and y = -2x + 3 are perpendicular. What is their mistake?

Two lines are parallel if they are in the same plane and never intersect. Mathematically, this means their slopes must be

Which form is Ax + By = C?

In the equation y = -4x + 7, what is the y-intercept?

What is the slope of y = -3?

The x-intercept of a line is the point where the graph crosses the x-axis. At this point, what is always the value of y?

In the context of a graph, slope is often described as the ratio of the vertical change to the horizontal change. What is the common nickname for this?

Equation of a line perpendicular to y = 3x through (0,0).

Solve for x: \((x + a) / b = (x - b) / a\)

A system has one solution. If the first line has a slope of 3, which of the following MUST be true about the second line?

Find the x-intercept of 3x - y = 9.

Convert y + 1 = -2(x - 4) to slope-intercept form.

For the horizontal line y = -3, what is the x-intercept?

In an isosceles triangle, the vertex angle is 40°. Find the base angles.

Slope of x = -100?

The solution to a system of equations on a graph is located at the ________ of the two lines.

A line with an undefined slope passes through (7, -1). What is its x-intercept?

Slope of a line through (1, 1) and (2, 3) in y=mx+b form.

Parallel lines must have the same ______.

Line parallel to y = 10x - 1.

Which slope is perpendicular to m = -3/4?

Convert y - 2 = 4(x - 1) into Standard Form (Ax + By = C).

In the point-slope form y - y1 = m(x - x1), what does the 'm' represent?

Solve: \((x + 1) / 2 - (x - 1) / 3 = 2\)

Are y = x + 2 and y = -x + 2 perpendicular?

Solve: \(|x + 4| = |2x - 1|\)

Y-intercept of 4x + 2y = 12?

How many solutions exist for |x - 2| + 5 = 5?

Are y = 2x + 1 and y = 2x - 1 parallel?

Solve for y: \(3x - 4y = 12\)

Solve: \(1 - 2x = 9\)

If the slope of a line is positive, and the y-intercept is negative, in which quadrant will the x-intercept be located?

Which line is perpendicular to y = -2x + 1?

Find the perpendicular slope to m = -0.1.

Find the slope of the line: \(y + 8 = -5(x - 2).\)

Find the y-intercept of the line 5x - 2y = 10.

Slope between (4, 3) and (8, 3)?

If two equations in a system represent the exact same line, the system is said to have

A student solves a system and gets '0 = 5'. What does this result indicate?

Solve for y in terms of x: \(2x + y = 10\)

Which point lies on y - 1 = 2(x + 3)?

Solve: \(|x/2 - 1| = 3\)

If a line has a slope of 4, what is the slope of a line that is perpendicular to it?

Solve: \((x/4) + (x/3) = 7\)

A line that is perfectly flat (horizontal) has which type of slope?

Write the equation in y = mx + b form for points (0, 3) and (2, 7).

Convert 2x - y = 5 into slope-intercept form (y = mx + b).

Identify the point and slope from: \(y + 2 = 0.5(x - 7)\)

If a line goes 'downhill' from left to right, what kind of slope does it have?

Convert 4x + 6y = 12 to slope-intercept form.

Find the slope perpendicular to a horizontal line.

The length of a rectangle is 3cm more than the width. If the perimeter is 26cm, find the width.

Are the lines 2x + 3y = 6 and 3x - 2y = 8 perpendicular?

A plumber charges $50 for a visit plus $30 per hour. Which equation represents the total cost (C) for (h) hours?

Line parallel to y = -4x + 1.

Two joggers start at the same point and run in opposite directions. One runs at 6 mph, the other at 8 mph. When will they be 21 miles apart?

Which point is the solution to the system { x - y = 4 ; x + y = 10 }?

Find slope: \((-1, -1) and (1, 1).\)

X-intercept of y = x - 5?

Two angles are supplementary. One is triple the other. Find the smaller angle.

A two-digit number ends in 5. The sum of digits is 1/7 of the number. Find the number.

Solve for m: \(y = mx + b\)

In the Standard Form Ax + By = C, which of the following is usually a requirement for the coefficient A?

Slope perpendicular to m = 1/3.

Does the point (1, 5) satisfy the equation y = 2x + 3?

Parallel slope to m = 1.

Solve: \(5(x + 1) = 5x + 1\)

What is the slope of the line passing through (5, -3) and (2, -3)?

Find the x-intercept of 2x + 4y = 8.

Convert 2x - y = 5 to slope-intercept form.

What is the x-intercept of x = -2?

An exterior angle of a triangle is 110°. One interior opposite angle is 40°. Find the other interior opposite angle.

The sum of four consecutive integers is 66. Find the smallest.

When you multiply the slopes of two perpendicular lines (that are not vertical or horizontal), the product is always

What is the slope of x = 10?

The sum of the digits of a 2-digit number is 9. Reversing the digits increases it by 27. Find the number.

Write in slope-intercept form: \(m = 1/2, through (0, 5).\)

Solve: \(2(x + 3) = 2x + 6\)

Point-slope through (-1, -1) with m = 5.

Find the slope (m) between (1, 2) and (3, 6).

A student solves 4x = 2 and says x = 2. What was the error?

Find k if 4x - 9 = kx + 2 has no solution.

X-intercept of 2x - y = 4?

If y = 3, what is the slope?

If a line has a slope of 2/3, what is the slope of a perpendicular line?

Solve: \((2/5)x - 1 = (1/10)x + 2\)

Are x = 2 and x = 5 parallel?

I drive 60 miles at 30 mph and 60 miles at 60 mph. What is the total travel time?

Convert y - 5 = 4(x + 2) to Standard Form.

A student calculates slope between (1, 2) and (3, 10) as (3 - 1) / (10 - 2) = 2/8. What was the error?

Find the slope of a line passing through (4, 7) and (4, -2).

Slope between (1, 1) and (2, 2)?

Point-slope form of a line with m=4 through (2, 2).

Is (2, 3) a solution to the system: \(x + y = 5 and 2x - y = 1?\)

Line A has a slope of -5. If Line B is parallel to Line A, what is its slope?

Slope perpendicular to m = 10.

Find the y-intercept of 2x + 5y = 20.

Find the slope: \((0, 0) and (5, 5).\)

In the equation y = 4x - 7, what is the y-intercept?

X-intercept of y = 2x + 10?

Convert 7x + y = 14 to slope-intercept form.

Parallel slope to m = 0.75.

Find the slope of y = x.

When two lines in a system are parallel and never touch, how many solutions does the system have?

Y-intercept of y = 3x - 1?

Solve: \(|x - 4| = 2x + 1\)

Which of the following is perpendicular to the vertical line x = -4?

For the vertical line x = 4, what is the y-intercept?

Perpendicular slope to m = -1.

Find slope: \((10, 5) and (12, 4).\)

Convert 15x + 3y = 9 to slope-intercept form.

The sum of three consecutive odd integers is 51. What is the middle integer?

Y-intercept of x + y = 10?

Are 2x + y = 4 and y = -2x + 8 parallel?

A car leaves at 40 mph. 1 hour later, a second car leaves at 60 mph. How long after the second car starts will it catch the first?

Solve for x: \(m(x - n) = p(x + q)\)

Find a line parallel to y = 2x - 3 passing through the origin (0,0).

A student converts y - 2 = 3(x - 1) to y = 3x - 1. What was their mistake?

Y-intercept of y = -x - 4?

Solve: \(2|x + 3| - 4 = 10\)

Line perpendicular to y = 1/5x + 2.

The y-intercept of a line is the point where the graph crosses the y-axis. At this point, what is always the value of x?

The formula for perimeter is P = 2L + 2W. Solve for W.

Calculate the slope of the line passing through (-2, 4) and (1, 10).

The slope of Line J is -2/7. To find the perpendicular slope, you flip the fraction and change the sign. What is the result?

Find the equation of a line parallel to y = 4x + 1 that passes through (0, -3).

A boat travels 12 mph in still water. If the river current is 3 mph, how long is a 45-mile trip upstream?

A line that goes straight up and down (vertical) has which type of slope?

Y-intercept of y = 0.5x + 3?

What is the slope of 0.2x - 0.2y = 1?

Slope between (2, 1) and (4, 2)?

Slope of a line perpendicular to 3x + y = 5.

Find the slope of 3x - 4y = 12.

An angle is 20° less than its complement. Find the angle.

Find the x-intercept of the line y = 3x - 9.

Standard form of y - 3 = 0.5(x + 4).

Write an equation in point-slope form for a line with m = -1 through (0, 0).

Convert y - 10 = -1(x + 5) to slope-intercept.

If two lines in a system are parallel, how many solutions exist?

Solve the formula for h: \(V = πr²h\)

Slope parallel to m = -2/9.

John can paint a room in 3 hours. Dave takes 6 hours. How long together?

If a line has a slope of 0 and passes through (2, 5), what is its equation?

What is the constant 'C' in the standard form of y = 2x + 5?

Slope of a line parallel to 2x - 5y = 10.

Standard form of y = -4/5x + 2.

Slope of 12x + 4y = 24.

Are 4x - y = 2 and y = 4x + 7 parallel?

Slope of y = 10?

Solve: \(10 - x = 15\)

Find line parallel to y = -x + 4 through (0, 5).

Which equation format is known as Slope-Intercept form?

What is the slope of a vertical line like x = 5?

The units digit is double the tens digit. Reversing them increases the value by 18. Find the number.

What is the y-intercept of y = 12x?

Slope perpendicular to m = 5/6.

Which equation represents a line with slope 3 passing through (1, 4)?

A student simplifies an equation to 0 = 0. This means the original equation is a(n) ________.

Two towns are 300 miles apart. Car A (50 mph) and Car B (70 mph) drive toward each other. How long until they meet?

Which line is perpendicular to x = 4?

Are y = 0.5x and y = -2x perpendicular?

Solve: \(3(2x - 4) = 6x - 12\)

Convert y = 3x - 4 to Standard Form.

If two lines have the same slope AND the same y-intercept, which of the following is true?

Convert y = 2/3x - 1 to Standard Form (no fractions).

Solve for r: \(C = 2πr\)

Calculate the slope between (-1/2, 2) and (1/2, 5).

Perpendicular slope to m = 1/8.

X-intercept of 5x + 10y = 50?

Which line is perpendicular to y = 0 (the x-axis)?

What is the slope of 5x + 2y = 20?

In the equation Ax + By = C, what is this specific form called?

Find the equation of a line parallel to y = 4x + 1 through (0, -3).

Slope between (-5, 2) and (-5, 8)?

Solve: \(x / (x - 2) = 2 / (x - 2) + 1\)

Which represents the same line as y = 2x - 4?

Convert 10x - 2y = 8 to slope-intercept form.

Solve: \(5 / (2x - 3) = 2 / (x + 1)\)

What is the slope of the line 3x + 2y = 10?

Solve for c: \(1/a = 1/b + 1/c\)

Slope of a line parallel to y = -1/2x + 8.

Solve: \(|x - 5| = -2\)