Answer
D. y – 85 = 10(x – 8)
Explanation
First we are going to find the slope of the line equation that represents the situation. To do it we are using the slope formula:
[tex]m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]
where
[tex]m[/tex] is the slope of the line
[tex](x_{1},y_{1})[/tex] are the coordinates of the first point
[tex](x_{2},y_{2})[/tex] are the coordinates of the second point
From our table we can get the points (2, 25) and (4, 45) so [tex]x_{1}=2[/tex], [tex]y_{1}=25[/tex], [tex]x_{2}=4[/tex], and [tex]y_{2}=45[/tex]. Let's replace the values in our formula:
[tex]m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]
[tex]m=\frac{45-25}{4-2}[/tex]
[tex]m=\frac{20}{2}[/tex]
[tex]m=10[/tex]
Now that we have our slope, we are going to use the point slope formula:
[tex]y-y_{1}=m(x-x_{1})[/tex]
Since the slope of our line is positive 10, we can rule out answers A and C.
Since the line of answer B has the numbers 4 and 45, we are going to test the point (4, 45) in our point slope formula:
[tex]y-45=10(x-4)[/tex] Nope! Answer B is not correct.
Since the line of answer D has the numbers 8 and 85, we are going to test the point (8, 85) in our point slope formula:
[tex]y-85=10(x-8)[/tex] We got the same line, so D is the correct answer.
