Bluebook SAT Test Linear Functions 9

Question 1

A linear function f satisfies f(0) = 4 and f(3) = 13. What is the equation of f?

Accepted Answer

f(x) = 3x + 4

Answer

Slope = (13 − 4)/(3 − 0) = 3; y-intercept = 4, so f(x) = 3x + 4.

Question 2

What is the y-intercept of the line passing through (−2, 7) and (4, −5)?

Accepted Answer

3

Answer

Slope = (−5 − 7)/(4 − (−2)) = −12/6 = −2; using point (4, −5): −5 = −2(4) + b → b = 3.

Question 3

The linear function C(n) = 0.15n + 12 gives the monthly cost in dollars for n gigabytes of data used. What is the meaning of 12 in this context?

Accepted Answer

The fixed monthly base charge regardless of data used

Answer

In C(n) = 0.15n + 12, the constant 12 is the y-intercept — the cost when n = 0, meaning the base charge.

Question 4

Line q passes through (1, −1) and is parallel to y = 4x + 7. What is the equation of line q?

Accepted Answer

y = 4x − 5

Answer

Parallel lines share slope 4; using (1, −1): −1 = 4(1) + b → b = −5, so y = 4x − 5.

Question 5

If f(x) = ax + 6 and f(−2) = 0, what is the value of a?

Accepted Answer

3

Answer

0 = a(−2) + 6 → −2a = −6 → a = 3.

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