Question

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

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 solutions:
Given,
\[\Rightarrow 6x - 3y = 6\].
Now rearranging
\[\Rightarrow - 3y = 6 - 6x\]
Divide the whole equation by -3
\[\Rightarrow \dfrac{{ - 3}}{{ - 3}}y = \dfrac{6}{{ - 3}} + \dfrac{{ - 6}}{{ - 3}}x\]
\[ \Rightarrow y = 2x - 2\].
Now we have slope intercept form with slope m and y-intercept ‘c’ is \[y = mx + c\]. On comparing\[ \Rightarrow y = 2x - 2\] this with the general form we have,
Slope \[m = 2\] 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 \[6x - 3y = 6\]
\[\Rightarrow 6(0) - 3y = 6\]
\[\Rightarrow - 3y = 6\]
\[\Rightarrow y = \dfrac{6}{{ - 3}}\]
\[y = - 2\]. Thus the y-intercept is -2.
To find the x-intercept substitute the value of ‘y’ is zero the,
Put \[y = 0\] in \[6x - 3y = 6\]
\[\Rightarrow 6x - 3(0) = 6\]
\[\Rightarrow 6x = 6\]
\[x = 1\]. This is the x-intercept.

Thus the required answer is slope m = 2 and y-intercept is c = -2.

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 the slope of a line is basically the tangent of the angle the line makes with positive x-axis.