How do you find the slope and y intercept of #3x +4y = 5#?

1 Answer
Apr 29, 2018

Answer:

Slope: #-3/4#
#y#-intercept: #(0, 5/4)#

Explanation:

To find the slope of a standard equation, we need to make #y# by itself.

#3x + 4y = 5#

First, subtract #color(red)(3x)# from both sides of the equation:
#3x + 4y quadcolor(red)(-quad3x) = 5 quadcolor(red)(-quad3x)#

#4y = 5 - 3x#

Divide both sides by #color(red)4#:
#(4y)/color(red)4 = (5-3x)/color(red)4#

#y = 5/4 - (3x)/4#

The slope is the value multiplying the #x#, so the slope is #-3/4#.

#--------------------#

To find the #y#-intercept, we set #x# to be #0# and find the value of #y#:
#y = 5/4 - (3x)/4#

#y = 5/4 - (3(0))/4#

Simplify:
#y = 5/4 - 0#

#y = 5/4#

So the #y#-intercept is at #(0, 5/4)#.

Hope this helps!