To answer this question, we need to remember what the intercepts are in a line equation.
The intercepts of a line are those points where the lines pass through the x-axis - this is called the x-intercept - and, at this point, the corresponding value of y is equal to zero. Likewise, the y-intercept is the point where the line passes through the y-axis, and, at this point, the value for x = 0.
Therefore, we can find those intercepts as follows:
Finding the x-intercept
We have the line equation is:
[tex]-4x-2y=12[/tex]
If we have that y = 0, then:
[tex]-4x-2(0)=12\Rightarrow-4x=12[/tex]
|f we divide both sides by -4, we have:
[tex]-\frac{4x}{-4}=\frac{12}{-4}\Rightarrow x=-3[/tex]
Therefore, the x-intercept of this line is (-3, 0).
Finding the y-intercept
We can proceed similarly. This time, we need to have x = 0. Therefore, we have:
[tex]-4(0)-2y=12\Rightarrow-2y=12[/tex]
If we divide both sides by -2:
[tex]\frac{-2y}{-2}=\frac{12}{-2}\Rightarrow y=-6[/tex]
Therefore, the y-intercept is (0, -6).
Thus, we can graph the line using the points (which are the intercepts of the line): (-3, 0) and (0, -6).
We can see the two intercepts in the following graph:
