What are the intercepts of #-x+3y=-3#?

1 Answer
Mar 6, 2018

Answer:

The x-intercept is #(3,0)#.

The y-intercept is #(0,-1)#.

Explanation:

Given:

#-x+3y=-3# is a linear equation in standard form:

#Ax+By=C#.

X-intercept: value of #x# when #y=0#.

Substitute #0# for #y# and solve for #x#.

#-x+3(0)=-3#

#-x=-3#

Multiply both sides by #-1#.

#x=3#

The x-intercept is #(3,0)#.

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Y-intercept: value of #y# when #x=0#

Substitute #0# for #x# and solve for #y#.

#0+3y=-3#

#3y=-3#

Divide both sides by #3#.

#(color(red)cancel(color(black)(3))^1y)/(color(red)cancel(color(black)(3))^1)=-color(red)cancel(color(black)(3))^1/color(red)cancel(color(black)(3))^1#

#y=-1#

The y-intercept is #(0,-1)#.

You can graph this equation by plotting the x- and y-intercepts and drawing a straight line through them.

graph{-x+3y=-3 [-11.25, 11.25, -5.625, 5.625]}