Question

What is the equation of the line, in slope-intercept form, that passes through (3, -1) and (-1, 5)? y = - 2y = -3x + 7 2x + 3y - 7 = 0

Answer 1

The line passing through (3, -1) and (-1, 5) has this slope:

5+1

m = ---------- = -3/2

-1-3

We need to find the y-intercept. To do this, substitute the knowns (-3/2 for m, -1 for y and 3 for x) into the slope-intercept equation:

-1 = (-3/2)(3) + b. Then: -1 = -9/2 + b, and so b = 9/2 - 1 = 7/2.

The desired equation is y = (-3/2)x + 7/2.

Answer 2

Answer: $y=\dfrac{-3}{2}x+\dfrac{7}{2}$

Step-by-step explanation:

The equation of a line passing through points (a,b) and (c,d) is given by :-

$(y-b)=\dfrac{d-b}{c-a}(x-a)$

The slope intercept form of a line is given by :-

$y=mx+c$

Given : The points from which line is passing : (3, -1) and (-1, 5)

Then , the equation of the line, in slope-intercept form, that passes through (3, -1) and (-1, 5) will be :-

$(y-(-1))=\dfrac{5-(-1)}{-1-3}(x-3)\\\\\Rightarrow\(y+1)=\dfrac{6}{-4}(x-3)\\\\\Rightyarrow\ y+1=\dfrac{-3}{2}x+\dfrac{9}{2}\\\\\Rightarrow\ y=\dfrac{-3}{2}x+\dfrac{9}{2}-1\\\\\Rightarrow\ y=\dfrac{-3}{2}x+\dfrac{7}{2}$