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:
[tex]y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)[/tex]
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:
[tex]\begin{gathered} y-y_{1}=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}(x-x_{1}) \\ \\ y-0=\frac{6-0}{4-(-2)}(x-(-2)) \\ \\ y=\frac{6}{4+2}(x+2) \\ \\ y=\frac{6}{6}(x+2) \\ \\ y=x+2 \end{gathered}[/tex]
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).
