Question

Hello! I need a little bit of help with this question please! (This is not from an active test, it is from a book I am using to study for my ASVAB.)

Answer 1

We have that the following two points lie on the line:

• (-2, 0) and (4, 6)

And we need to find the equation of the line that passes through both points.

To find the equation of the line, we can proceed as follows:

1. Apply the two-point equation of the line, which is given by:

`y-y_1=(y_2-y_1)/(x_2-x_1)(x-x_1)`

2. We have to label both points as follows:

• (-2, 0) ---> x1 = -2, y1 = 0

• (4, 6) ---> x2 = 4, y2 = 6

3. Now, we can substitute the corresponding points into the two-point equation of the line:

`\begin{gathered} y-y_(1)=(y_(2)-y_(1))/(x_(2)-x_(1))(x-x_(1)) \\ \\ y-0=(6-0)/(4-(-2))(x-(-2)) \\ \\ y=(6)/(4+2)(x+2) \\ \\ y=(6)/(6)(x+2) \\ \\ y=x+2 \end{gathered}`

Therefore, we have that the slope of the line is m = 1, and the equation of the line is y = x + 2.

Therefore, in summary, the equation of the line is y = x + 2 (Option D).