Question

A linear function has an x-intercept of 12 and a slope of 3/8. How does this function compare to the linear function that is represented by the table? X= -2/3, -1/6, 1/3, 5/8. Y=-3/4, -9/16, -3/8, -3/16. 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.

Answer 1

We rewrite the statement correctly:
"A linear function has an y-intercept of 12 and a slope of 3/8"
Therefore, the linear function is:
y = (3/8) x + 12
We look for the linear function of the table:
y-yo = m (x-xo)
Where,
m = (y2-y1) / (x2-x1)
m = ((- 3/8) - (- 3/4)) / ((1/3) - (- 2/3))
m = ((- 3/8) - (- 6/8)) / (3/3)
m = ((- 3 + 6) / 8) / (1)
m = 3/8
(xo, yo) = (- 2/3, -3/4)
Substituting:
y + 3/4 = (3/8) (x + 2/3)
y = (3/8) x + 2/8 - 3/4
y = (3/8) x + 1/4 - 3/4
y = (3/8) x + -2/4
y = (3/8) x + -1/2
The lines are:
y = (3/8) x + 12
y = (3/8) x + -1/2
Answer:
It has the same slope and a different y-intercept