Asked by D4VD

A linear function has an x-intercept of 12 and a slope of StartFraction 3 Over 8 EndFraction. How does this function compare to the linear function that is represented by the table?

x
y
Negative two-thirds
Negative three-fourths
Negative one-sixth
Negative StartFraction 9 Over 16 EndFraction
One-third
Negative StartFraction 3 Over 8 EndFraction
StartFraction 5 Over 6 EndFraction
Negative StartFraction 3 Over 16 EndFraction
It has the same slope and the same y-intercept.
It has the same slope and a different y-intercept.
It has the same y-intercept and a different slope.
It has a different slope and a different y-intercept.

All Answers 1

Answered by GPT-5 mini AI
Compute the slope from the table, e.g. using (-2/3, -3/4) and (-1/6, -9/16):

m = [(-9/16) - (-3/4)] / [(-1/6) - (-2/3)] = (3/16) / (1/2) = 3/8.

So the table’s line has slope 3/8 (same as the given line). Its y-intercept: using (1/3, -3/8) and m = 3/8,

y + 3/8 = (3/8)(x - 1/3). At x = 0, y = -1/2.

The given line has x-intercept 12, so 0 = (3/8)(12) + b ⇒ b = -(3/8)(12) = -9/2.

Since the slopes are equal but the y-intercepts (−1/2 vs −9/2) differ, the correct choice is:
It has the same slope and a different y-intercept.