Question

What is the slope and y-intercept of $x + 3y = 6$?

Answer 1

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 solution:
Given,
$x + 3y = 6$.
Now rearranging
$3y = - x + 6$
Divide the whole equation by 3
$\Rightarrow y = - \dfrac{1}{3}x + 2$.
Now we have slope intercept form with slope m and y-intercept ‘c’ is $y = mx + c$. On comparing
$y = - \dfrac{1}{3}x + 2$ this with the general form we have,
Slope $m = - \dfrac{1}{3}$ and y-intercept $c = 2$ .

Additional information:
We can also find the y-intercept by putting the value of x is equal to zero.
Put $x = 0$ in $x + 3y = 6$
$0 + 3y = 6$
$3y = 6$
Divide the whole equation by 3
$y = \dfrac{6}{3}$
$\Rightarrow y = 2$. Thus the y-intercept is 2.

To find the x-intercept substitute the value of ‘y’ is zero the,
Put $y = 0$ in $x + 3y = 6$
$x + 3(0) = 6$
$\Rightarrow x = 6$. This is the x-intercept.

Note:
We know that x and y intercept basically refer to the points where the line cuts the x-axis and y-axis of the graph. The point where coordinate cuts the line at x-axis is x-intercept and y-axis is y-intercept. We know that slope of a line is basically the tangent of the angle the line makes with positive x-axis.