How do you graph #y=2/3x-4#?

1 Answer
Mar 10, 2018

Answer:

Refer to the explanation.

Explanation:

Graph:

#y=2/3x-4# is the slope-intercept form of a linear equation:

#y=mx+b,#

where:

#m# is the slope and #b# is the y-intercept.

You need two points on the line. Let one of the points be the x-intercept and the other point be the y-intercept.

The y-intercept is #-4# (from the equation), which is the value of #y# when #x=0#. So the point is #(0,-4)#.

The x-intercept is the value of #x# when #y=0#.

To determine the x-intercept, substitute #0# for #y# and solve for #x#.

#0=2/3x-4#

Multiply both sides by #3#.

#3xx0=color(red)cancel(color(black)(3))^1xx2/color(red)cancel(color(black)(3))^1x-4xx3#

Simplify.

#0=2x-12#

Add #12# to both sides.

#12=2x#

Divide both sides by #2#.

#color(red)cancel(color(black)(12))^6/color(red)cancel(color(black)(2))^1=(color(red)cancel(color(black)(2))^1x)/color(red)cancel(color(black)(2))^1#

Simplify.

#6=x#

#x=6#

The x-intercept is #(6,0)#.

Plot the x- and y-intercepts and draw a straight line through them.

graph{y=2/3x-4 [-10, 10, -5, 5]}