Bluebook SAT Test Linear Functions 1

Question 1

A line passes through the points (2, 5) and (6, 13). What is the slope of the line?

Accepted Answer

2

Answer

Slope = (13 − 5)/(6 − 2) = 8/4 = 2.

Question 2

The function f(x) = 3x − 7 gives the profit (in dollars) a vendor earns when selling x items. What does the value 3 represent in this context?

Accepted Answer

The profit per item sold

Answer

In f(x) = mx + b, the slope m = 3 is the rate of change, i.e., the profit earned per each additional item sold.

Question 3

Which equation represents a line with a slope of −2 and a y-intercept of 5?

Accepted Answer

y = −2x + 5

Answer

Slope-intercept form is y = mx + b where m = −2 and b = 5, giving y = −2x + 5.

Question 4

A car rental company charges a flat fee of $30 plus $0.25 per mile driven. Which function models the total cost C(m) for m miles?

Accepted Answer

C(m) = 0.25m + 30

Answer

The flat fee is the y-intercept (30) and the per-mile rate is the slope (0.25), so C(m) = 0.25m + 30.

Question 5

If f(x) = −4x + 11, what is the value of f(3)?

Accepted Answer

−1

Answer

f(3) = −4(3) + 11 = −12 + 11 = −1.

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