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.