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=(-3)/(2)x+(7)/(2)`

Explanation:

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

`(y-b)=(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))=(5-(-1))/(-1-3)(x-3)\\\\\Rightarrow\(y+1)=(6)/(-4)(x-3)\\\\\Rightyarrow\ y+1=(-3)/(2)x+(9)/(2)\\\\\Rightarrow\ y=(-3)/(2)x+(9)/(2)-1\\\\\Rightarrow\ y=(-3)/(2)x+(7)/(2)`