Question

What is the slope and y-intercept of \[x + 3y = 6\]?

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 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.