Linear Functions Flashcards

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

Answer: 2

Slope = (13 − 5)/(6 − 2) = 8/4 = 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?

Answer: The profit per item sold

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

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

Answer: y = −2x + 5

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

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?

Answer: C(m) = 0.25m + 30

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

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

Answer: −1

f(3) = −4(3) + 11 = −12 + 11 = −1.

The table below shows values for a linear function g(x). x: 0 1 2 3 g: 7 10 13 16 What is the value of g(10)?

Answer: 37

The slope is 3 and the y-intercept is 7, so g(x) = 3x + 7; g(10) = 30 + 7 = 37.

Line ℓ has the equation 4x − 2y = 10. What is the x-intercept of line ℓ?

Answer: (5/2, 0)

Set y = 0: 4x = 10 → x = 5/2, so the x-intercept is (5/2, 0).