Linear Equations Chapter

If 4x + 5 is 4 less than 10, what is the value of 2x?

• 1/4

• 1/2

• 4

• 8

In the xy‑plane to the left, a point (not shown) with coordinates (a, b) lies on the graph of the linear function h. If a and b are positive integers, what is the ratio of a to b?

• 2:3

• 3:2

• 5:6

• 6:5

Answer explanation

Remember that, in a line, any two pair of points (x, y) lying on the line will give the same value for the slope of the line.

Observe that the line passes through (0, 0) and (6, 5).

Using these two points, find the value of the slope.

• (-14, -6)

• (-6, -14)

• (-6, 14)

• (14, 6)

Sara is waiting in line to ride the amusement park’s newest roller coaster. The number of people in front of her can be represented by the equation P = 34 − 2m, where P is the number of people in front of her and m is the number of minutes Sara has waited in line. What is the meaning of the value 34 in this equation?

• Sara will reach the front of the line within 34 minutes.

• Sara started with 34 people in front of her.

• Sara moves up in the line at a rate of 34 people per hour.

• Sara moves up in the line at a rate of 34 people per minute.

What is the y-intercept of 2x - 5y = 35?

• (0,-7)

• (-7,0)

• (35/2, 0)

• (0,35/2)

A line passes through the origin and points (−4, c) and (c, −9). What is one possible value of c?

• 4

• 6

• 9

• 12

Answer explanation

Use the origin and each of the points to get two expressions for the slope of the line.

Equate both the expressions (involving c) to get the possible values of c.

Sunjay is traveling to a national park. The number of miles he needs to travel can be represented by the equation M = 172 − 57h, where M is the number of miles to the national park and h is the number of hours Sunjay has to travel. What is the meaning of the value 57 in this equation?

• Sunjay started at a distance 57 miles from the national park.

• Sunjay will reach the national park in 57 hours.

• Sunjay travels to the national park at a rate of 57 miles per hour.

• Sunjay has traveled 172 miles in 57 hours.

What is the equation of the line connecting the midpoint of line segment AB with point C in the figure?

• y = −2x − 2

• y = −2x + 5

• y = 2x − 2

Line y = mx + 5 passes through point (a, b), where a ≠ 0 and b ≠ 0. If m is a constant, what is the slope of the line in terms of a and b?

Julius has budgeted $150 per month for electricity. Last month his electricity bill was $190 based on a rate of $0.12 per kilowatt hour. Which of the equations below represents the number of kilowatt hours, k, by which Julius needs to reduce his electricity usage this month in order to meet his budget?

• 0.12k = 40

• 0.12k = 150

Answer explanation

We need to reduce the amount spent by 40$ (Because, 190-40 = 150).

If k is the number of hours we need to reduce (the rate is constant, which is 0.12), then 0.12*k will give us the number of dollars which should be equal to 40.