How do you find the slope and intercept of #y = 4/3x - 3#?

2 Answers
Aug 2, 2018

Answer:

The slope is #4/3#.

The #x#-intercept is at #(9/4, 0)#.

The #y#-intercept is at #(0, -3)#.

Explanation:

#y = 4/3x - 3#

This equation is in slope-intercept form:

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We know the slope is the value multiplied by #x#, so the slope is #4/3#.

To find the #x-#intercept, plug in #0# for #y# and solve for #x#:
#0 = 4/3x - 3#

Add #color(blue)3# to both sides:
#0 quadcolor(blue)(+quad3) = 4/3x - 3 quadcolor(blue)(+quad3)#

#3 = 4/3x#

Multiply both sides by #color(blue)(3/4)#:
#3 color(blue)(*3/4) = 4/3x color(blue(*3/4)#

#9/4 = x#

#x = 9/4#

Therefore, the #x#-intercept is at #(9/4, 0)#.

To find the #y#-intercept, plug in #0# for #x# and solve for #y#:
#y = 4/3(0) - 3#

#y = 0 - 3#

#y = -3#

Therefore, the #y#-intercept is at #(0, -3)#.

Hope this helps!

Aug 2, 2018

Answer:

Slope #4/3#, #x#-int #9/4#, #y#-int #-3#

Explanation:

This equation is in slope-intercept form

#y=mx+b#, with slope #m# and a #y#-intercept of #b#. By pattern matching, we see our slope is #4/3# and our #y#-intercept is #-3#.

We can find the #x#-intercept by setting #y# equal to zero. We get

#0=4/3x-3=4/3x=3=>x=9/4#

Therefore, our slope is #4/3#, our #y#-intercept is #-3#, and our #x#-intercept is #9/4#.

Hope this helps!