To write the equation of the line that passes through the points (1, 60) and (7, 140), we first need to determine the slope (m) of the line using the formula:
\[ m = \frac{y_2 - y_1}{x_2 - x_1} \]
Let \((x_1, y_1) = (1, 60)\) and \((x_2, y_2) = (7, 140)\).
Substituting in the coordinates:
\[ m = \frac{140 - 60}{7 - 1} = \frac{80}{6} = \frac{40}{3} \]
Now that we have the slope \(m = \frac{40}{3}\), we can use the point-slope form of the equation of a line, which is:
\[ y - y_1 = m(x - x_1) \]
Using the point (1, 60):
\[ y - 60 = \frac{40}{3}(x - 1) \]
Now, we can distribute the slope \(\frac{40}{3}\):
\[ y - 60 = \frac{40}{3}x - \frac{40}{3} \]
Now, add 60 to both sides:
\[ y = \frac{40}{3}x - \frac{40}{3} + 60 \]
To simplify \(60\) in terms of thirds:
\[ 60 = \frac{180}{3} \]
So:
\[ y = \frac{40}{3}x - \frac{40}{3} + \frac{180}{3} \]
Combine the constants:
\[ y = \frac{40}{3}x + \frac{140}{3} \]
Thus, the equation of the line is:
\[ y = \frac{40}{3}x + \frac{140}{3} \]