For the function rule y = -2x - 3, provide the x-y coordinates of the y-intercept and the x-intercept.

Question

gavlois1 · Answer

For functions of the format:

$$y = mx+b$$

m is equal to the slope of the line while b is actually the y-intercept. So right from the start, we can tell that from:

$$y = -2x-3$$

-2 is the slope (if required) and -3 is the y-intercept. 

To solve for the x,y coordinates of the y variable to -3 to find its x counterpart:

$$y = -2x-3$$
$$-3 = -2x -3$$
We move the -3 on the right side to the left:

$$-3 + 3 = -2x$$
$$0 = -2x$$

Divide both sides by -2:

$$\frac{ 0 }{ -2 } = \frac{ -2x }{ -2 }$$

Therefore, the x-coordinate of the y-intercept is 

$$0 = x$$

Then we can safely say the coordinates of the y-intercept is (0,-3). However, the easiest way to do this is that we know intercepts are always on the axis, therefore the other coordinate is 0. y-intercepts have an x coordinate of 0 and x-intercepts have a y coordinate of 0.

Using that idea, we can solve for the x -intercept. We set y to 0 since the intercept calls for the point of intersection at the x-axis. 

$$0 = -2x -3$$

$$3 = -2x$$
$$-\frac{ 3 }{ 2 }=x$$

And so, we can say that the coordinates of the x-intercept is (-3/2 , 0)