# How do you find a standard form equation for the line with (-6, 0) and (2, -9)?

##### 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.We have to find the values of m and b.

To calculate 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)" are 2 coordinate points"# here the 2 points are (-6 ,0) and (2 ,-9)

let

# (x_1,y_1)=(-6,0)" and " (x_2,y_2)=(2,-9)#

#rArrm=(-9-0)/(2+6)=(-9)/8=-9/8# We can now write a

partial equationas#y=-9/8x+b# To calculate b, use either of the 2 given points that lie on the line.

Using (2 ,-9)That is x= 2 and y = -9 , substitute in

partial equation

#rArr(-9/8xx2)+b=-9rArr-9/4+b=-9rArrb=-27/4#

#rArry=-9/8x-27/4" is the equation of the line"#