Question

What is the y-intercept for the equation \[4x - 3y = - 18\] ?

Answer 1

Hint: We will use the general equation of a line which is given by \[y = mx + c\] . That is the slope intercept form. Here ‘m’ is called slope and ‘c’ is called y-intercept. We convert the given equation into the slope intercept form and we compare it to get the desired result.

Complete step-by-step answer:
Given,
 \[4x - 3y = - 18\] .
Now rearranging we have,
 \[ - 3y = - 18 - 4x\]
Divide the whole equation by -3 we have,
 \[y = \dfrac{{ - 18}}{{ - 3}} + \dfrac{{ - 4}}{{ - 3}}x\]
 \[y = 6 + \dfrac{4}{3}x\]
 \[ \Rightarrow y = \dfrac{4}{3}x + 6\] .
Now we have slope intercept form with slope m and y-intercept ‘c’ is \[y = mx + c\] . On comparing \[ \Rightarrow y = - 4x + 7\] this with the general form we have,
Slope \[m = \dfrac{4}{3}\] and y-intercept \[c = 6\]
So, the correct answer is “ \[c = 6\] ”.

Note: We can also find the y-intercept by putting the value of x is equal to zero.
Put \[x = 0\] in \[4x - 3y = - 18\]
 \[4\left( 0 \right) - 3y = - 18\]
 \[ - 3y = - 18\]
Divide by -3 on both sides we have,
 \[y = \dfrac{{ - 18}}{{ - 3}}\]
 \[y = 6\] . Thus the y-intercept is 6.
To find the x-intercept substitute the value of ‘y’ is zero the,
Put \[y = 0\] in \[4x - 3y = - 18\]
 \[4x - 3(0) = - 18\]
 \[4x = - 18\]
Divide the whole equation by 4
 \[x = \dfrac{{ - 18}}{4}\] .
 \[x = \dfrac{{ - 9}}{2}\]
This is the x-intercept.