How do you write the slope-intercept form of the equation of the line that goes through (2, -2) and (0, 3)?

1 Answer
Nov 17, 2016

y=-5/2x+3

Explanation:

Slope intercept form of a line is:

y=mx+b

Where m is the slope and b is the y intercept

To write an equation using two sets of points, you first have to ind the slope:

m=(y_2-y_1)/(x_2-x_1)

Where
(2,-2)=>(x_1,y_1)

and

(0,3)=>(x_2,y_2)

m=(3+2)/(0-2)=-5/2

Next, pick a set of points and plug them into point slope formula using the slope of -5/2:

y-y_1=m(x-x_1)

y+2=-5/2(x-2)

Distribute the -5/2 throughout the set of parenthesis

y+2=-5/2x+5

Subtract 2 on both sides of the parenthesis

y=-5/2x+3

If you were to use the other set of parenthesis, (0,3), the equation should be the same

y-3=-5/2(x-0)

Distribute the -5/2 throughout the set of parenthesis

y-3=-5/2+0

Add 3 on both sides of the equation

y=-5/2+3