Question

Write an equation in point-slope form for the line through thr given point with the given slope:

(-3,5); m=2/3

A. y + 3 = 2/3(x-5)

B. y + 5 = (2/3)(x+3)

C. y - 5 = 2/3(x-3)

D. y - 5 = 2/3(x+3)

Answer 1

D

Explanation:

The equation of a line in point- slope form is

y - b = m(x - a)

where m is the slope and (a, b) a point on the line

here m =
`(2)/(3)` and (a, b) = (- 3, 5), hence

y - 5 =
`(2)/(3)`(x + 3) → D

Answer 2

D. y - 5 = 2/3(x + 3)

Explanation:

The point-slope form of an equation of a line:

`y-y_1=m(x-x_1)`

We have the slope 2/3 an the point (-3, 5). Substitute:

`y-5=(2)/(3)(x-(-3))\\\\y-5=(2)/(3)(x+3)`