Question

What is an equation of a line, in point-slope form, that passes through (1, −7) and has a slope of −2/3 ?

A. y+7=−23(x−1)y+7=−23(x−1)

B. y−7=23(x−1)y−7=23(x−1)

C. y−7=−23(x+1)y−7=−23(x+1)

D. y+7=23(x+1)y+7=23(x+1)

Answer 1

y-y1=m(x-x1)

substitute

y+7=-2/3(x-1)
y+7=2/3(-x+1)
or
y+7=-2/3x +2/3


i have no idea what those options are for but the most likely answer looks like option A

Answer 2

Answer:- A. $y+7=\frac{-2}{3}(x-1)$

Explanation:-

We know that the equation of a line passing through point (a,b) whose slope is m, is

$(y-b)=m(x-a)$

Thus, the equation of a line passing through point (1, −7) whose slope $\frac{-2}{3}$ is ,

$(y-(-7))=\frac{-2}{3}(x-1)$

$\\\Rightarrow(y+7)=\frac{-2}{3}(x-1)$

∴ A. is the right answer. The equation of a line passing through point (1, −7) whose slope $\frac{-2}{3}$ is $(y+7)=\frac{-2}{3}(x-1)$.