# How do you find the slope and intercept of #5 - 1/3y = 2x#?

##### 1 Answer

Aug 28, 2016

slope = - 6 , y-intercept = +15

#### 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.The advantage to having the equation in this form is that m and b , may be extracted 'easily'.

Rearrange

#5-1/3y=2x" in this form"# subtract 5 from both sides.

#rArrcancel(5)-cancel(5)-1/3y=2x-5rArr-1/3y=2x-5# multiply through by - 1 :

#1/3y=-2x+5# now multiply both sides by 3.

#rArrcancel(3)^1xx1/cancel(3)^1 y=-6x+15rArry=-6x+15# The equation is now in the form

#color(blue)(y=mx+b)#

#rArr"slope" =-6" and y-intercept" =+15#

graph{-6x+15 [-45.63, 45.6, -22.74, 22.9]}