Find the line equation in slope-intercept form

Question

Find the line passing through the points (2,-4) and (5,2).?

Answer 1

Slope intercept form line equation is y = mx + c.   m is slope and c is y-intercept.

m =( y2-y1)/(x2-x1) = (2-(-4)/(5-2) = 6 / 3 = 2

The line equation is y = 2x + c.

find the y-intercept value by substituting (5, 2) in y = 2x + c.

2 = 2 * 5 + c

c = 2 - 10= -8

Substitute c = -8 in line equation.

the line equation is y = 2x - 8

Standard form line equation is Ax+By = c.

Subtract y from each side.

y - y = 2x - y - 8

Add 8 to each side.

2x - y = 8

The line equation in slope-intercept form is y = 2x - 8.

The line equation in standard form is 2x - y = 8.

Answer 2

Given points are (2 , -4) and (5 , 2) 

(x1 , y1) = (2 , -4) and ( x2 , y2) = (5 , 2)

Slope of the line equation is

m = 2

The general form of line equation is y = mx + c

Substitute values

m = 2 and (x , y) = (2 , -4)

y = mx + c

-4 = 2 ( 2) + c

-4 = 4 + c

c = -4  - 4

c = -8

Therefore the required  line equation is y = 2 x - 8