What is the #y#-intercept of the line #3x-4y=24#?

Question

Julia Adams · Accepted Answer

See a solution process below:

This equation is in Standard Linear form. The standard form of a linear equation is: #color(red)(A)x + color(blue)(B)y = color(green)(C)# Where, if at all possible, #color(red)(A)#, #color(blue)(B)#, and #color(green)(C)#are integers, and A is non-negative, and, A, B, and C have no common factors other than 1 The slope of an equation in standard form is: #m = -color(red)(A)/color(blue)(B)# The #y#-intercept of an equation in standard form is: #color(green)(C)/color(blue)(B)# #color(red)(3)x - color(blue)(4)y = color(green)(24)# Or #color(red)(3)x + color(blue)(-4)y = color(green)(24)# Substituting the values from the equation gives the #y#-intercept as: #color(green)(24)/color(blue)(-4) = -6# or #(0, -6)#

Eva Adamson · Answer

#(0,-6)# Rearrange #3x=4y+24# #3x-24=4y# #y=3/4x-6#

Kennedy Adams · Answer

#(0,-6)#

The #y#-intercept is when #x# is equal to zero, so let's just plug zero into our equation for #x#.

The #x# term will just disappear, and we're left with

#-4y=24=>y=-6#

Dividing both sides by #-4#, we find that the #y#-intercept of the line occurs at #(0,-6)#.

The nice thing about standard form equations of lines is that finding the intercepts is a simple process.

To find the #y#-intercept, set #x# equal to zero.

To find the #x#-intercept, set #y# equal to zero.

I hope this is useful.

Eli Assouline · Answer

undefined To find the y-intercept of the line 3x - 4y = 24, set x = 0 and solve for y.
When x = 0:
3(0) - 4y = 24
-4y = 24
y = -6
So, the y-intercept is -6.