MATH SOLVE

4 months ago

Q:
# 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.

Accepted Solution

A:

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

"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