Linear Functions Flashcards

The linear function h models the height (in feet) of a balloon t minutes after launch: h(t) = 120 + 15t. What is the height of the balloon after 8 minutes?

Answer: 240 feet

h(8) = 120 + 15(8) = 120 + 120 = 240 feet.

What is the x-intercept of the line with equation 3x + 5y = 15?

Answer: (5, 0)

Set y = 0: 3x = 15 → x = 5, so the x-intercept is (5, 0).

Two linear functions are defined as f(x) = 2x + 3 and g(x) = 2x − 5. Which of the following is true about their graphs?

Answer: They are parallel (never intersect)

Both functions have slope 2 but different y-intercepts, so their graphs are parallel lines that never intersect.

A student earns $12.50 per hour working part-time. If the student works h hours and has already saved $75, which function gives the total savings S(h)?

Answer: S(h) = 12.50h + 75

The initial savings ($75) is the y-intercept and the hourly rate ($12.50) is the slope: S(h) = 12.50h + 75.

Line m has the equation x = −4. Which of the following best describes this line?

Answer: A vertical line at x = −4

Equations of the form x = k represent vertical lines passing through (k, 0) on the x-axis.

If g(x) = mx + 4 and g(5) = 19, what is the value of m?

Answer: 3

19 = m(5) + 4 → 5m = 15 → m = 3.

The table shows a linear relationship between x and y. x: −2 0 2 4 y: 1 5 9 13 Which equation represents this relationship?

Answer: y = 2x + 5

From the table, slope = (9 − 5)/(2 − 0) = 2 and y-intercept = 5, giving y = 2x + 5.