What are the intercepts of the line #y=9/2x - 4#?

1 Answer
May 9, 2018

Answer:

The y-intercept for the given line is #(0,-4)#.

The x-intercept is #(8/9,0)# or #(0.889,0)#.

Explanation:

Find the intercepts:

#y=9/2x-4#

This is a linear equation in slope-intercept form:

#y=mx+b#,

where:

#m# is the slope #(9/2)# and #b# is the y-intercept #(-4)#.

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

By definition, the y-intercept for the given line is #(0,-4)#.

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

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

#0=9/2x-4#

Add #4# to both sides.

#4=9/2x#

Multiply both sides by #2#.

#8=9x#

Divide both sides by #9#.

#8/9=x#

The x-intercept is #(8/9,0)# or #(0.889,0)#.

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

graph{y=9/2x-4 [-9.77, 10.23, -7.61, 2.39]}