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

Question

Avery Alexander · Accepted Answer

Slope: #-3/4#
#y#-intercept: #(0, 5/4)# 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)#. I hope this is useful.

Hazel Anglin · Answer

undefined To find the slope and y-intercept of the equation $3x + 4y = 5$, follow these steps:

1. Rewrite the equation in slope-intercept form $y = mx + b$ by isolating $y$:
   $4y = -3x + 5$
   Divide by 4: $y = -\frac{3}{4}x + \frac{5}{4}$
2. Compare the equation with $y = mx + b$ to identify the slope ($m$) and y-intercept ($b$):
   Slope ($m$) = -$\frac{3}{4}$
   Y-intercept ($b$) = $\frac{5}{4}$