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:
\(m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}\)
where
\(m\) is the slope of the line
\((x_{1},y_{1})\) are the coordinates of the first point
\((x_{2},y_{2})\) are the coordinates of the second point
From our table we can get the points (2, 25) and (4, 45) so \(x_{1}=2\), \(y_{1}=25\), \(x_{2}=4\), and \(y_{2}=45\). Let's replace the values in our formula:
\(m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}\)
\(m=\frac{45-25}{4-2}\)
\(m=\frac{20}{2}\)
\(m=10\)
Now that we have our slope, we are going to use the point slope formula:
\(y-y_{1}=m(x-x_{1})\)
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:
\(y-45=10(x-4)\) 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:
\(y-85=10(x-8)\) We got the same line, so D is the correct answer.
