How do you calculate the slope, x intercept, and y intercept of the following equation: #3x + 4y= 0#?

Question

How do you calculate the slope, x intercept, and y intercept of the following equation:  #3x + 4y= 0#?

Genesis Allen · Accepted Answer

Slope = -3/4
The x intercept is 0
The y intercept is 0

Method 1 : Convert to slope intercept form #color(white)("XXXX")#A linear equation in the form: #color(white)("XXXX")##color(white)("XXXX")##y = mx+b# #color(white)("XXXX")#is in slope intercept form with slope #=m# #color(white)("XXXX")#and y-intercept #=b# #3x+4y = 0# #rarr 4y = -3x + 0# #rarr y = -3/4x+0##color(white)("XXXX")#(slope intercept form with slope #-3/4# and y intercept #= 0# Substituting #y=0# into the original equation gives #x=0#, the x-intercept. Method 2: Use the slope formula for a standard form linear equation #color(white)("XXXX")#A linear equation in standard form: #color(white)("XXXX")##color(white)("XXXX")##Ax+By=C# #color(white)("XXXX")#has a slope of #-(A/B)# #color(white)("XXXX")#or, in this case #color(white)("XXXX")##color(white)("XXXX")#-3/4# The y-intercept is the value of y when #x=0# #rarr # y intercept # = 0# The x-intercept is the value of x when #y=0# #rarr # x intercept # =0#

Abigail Allen · Answer

undefined To calculate the slope, x-intercept, and y-intercept of the equation 3x + 4y = 0:

1. Slope: To find the slope, rewrite the equation in slope-intercept form (y = mx + b), where m is the slope:
   3x + 4y = 0
   4y = -3x
   y = (-3/4)x

Therefore, the slope (m) is -3/4.

2. X-intercept: To find the x-intercept, set y = 0 and solve for x:
   3x + 4(0) = 0
   3x = 0
   x = 0

Therefore, the x-intercept is (0, 0).

3. Y-intercept: To find the y-intercept, set x = 0 and solve for y:
   3(0) + 4y = 0
   4y = 0
   y = 0

Therefore, the y-intercept is (0, 0).