Question

Graph 4x + 8y = -16 using the x- and y-intercepts.

Answer 1

Y-intercept is located at point (0, -2).

X-intercept is located at point (-4, 0).

Explanation:

1. Write the function.

`4x + 8y = -16`

2. Find the y-intercept.

The y-intercept is the point where the line of the equation touches the y axis. In other words, it's the value of y when x=0. Hence, substitute x by 0 and calculate a value for y:

`4(0) + 8y = -16\\ \\8y=-16\\ \\(8y)/(8) =(-16)/(8) \\ \\y=-2`

3. Graph the y-intercept.

Y-intercept is located at point (0, -2). Check the first attached image to see the point in the plane.

4. Find the x-intercept.

This value can be found when y=0, opposite from the y-intercept. Substitute y by 0 and calculate x:

`4x + 8(0) = -16\\ \\4x=-16\\\\ (4x)/(4) =(-16)/(4) \\ \\x=-4`

5. Graph the x-intercept.

X-intercept is located at point (-4, 0). Check the second attached image to see the point in the plane.

6. Draw the line of the function.

Joining the 2 intercepts with a line will give the line that represents the equation. Check the third attached image to see the graphed line.

You may also extend the line infinitely, since the slope will not change in any value. Check the fourth attached image.