# How do you write the equation in slope intercept form given (-2,-8) and (2,-6)?

##### 1 Answer

#### Explanation:

The equation of a line in

#color(blue)"slope-intercept form"# is

#color(red)(|bar(ul(color(white)(a/a)color(black)(y=mx+b)color(white)(a/a)|)))#

where m represents the slope and b, the y-intercept.m and b have to be found to complete the equation of the line.

To find m use the

#color(blue)"gradient formula"#

#color(red)(|bar(ul(color(white)(a/a)color(black)(m=(y_2-y_1)/(x_2-x_1))color(white)(a/a)|)))#

where# (x_1,y_1)" and " (x_2,y_2)" are 2 coordinate points"# Here the 2 points are (-2 ,-8) and (2 ,-6)

let

# (x_1,y_1)=(-2,-8)" and " (x_2,y_2)=(2,-6)#

#rArrm=(-6-(-8))/(2-(-2))=2/4=1/2# The same result is obtained if the coordinate points are reversed.

The

partial equationis#y=1/2x+b# To find b, use either of the 2 given points and substitute in the partial equation.

Using (2 ,-8) with x = 2 and y = -8

#(1/2xx2)+b=-8rArr1+b=-8rArrb=-9#

#rArry=1/2x-9" is the equation"#