Answer
$y = -\frac{40}{7}x + \frac{660}{7}$
Work Step by Step
We are given the points $(13, 20)$ and $(6, 60)$.
Let's use the formula to find the slope $m$ given two points:
$m = \frac{y_2 - y_1}{x_2 - x_1}$
Let's plug in the values into this formula:
$m = \frac{60 - 20}{6 - 13}$
Subtract the numerator and denominator to simplify:
$m = \frac{40}{-7}$
Now that we have the slope, we can use one of the points and plug these values into the point-slope equation, which is given by the formula:
$y - y_1 = m(x - x_1)$
Let's plug in the points and slope into the formula:
$y - 20 = -\frac{40}{7}(x - 13)$
This equation is now in point-slope form. To change this equation into point-intercept form, we need to isolate $y$.
Use distribution to simplify:
$y - 20 = -\frac{40}{7}x - \frac{40}{7}(-13)$
Simplify by multiplying:
$y - 20 = -\frac{40}{7}x + \frac{520}{7}$
To isolate $y$, we add $20$ to each side of the equation:
$y = -\frac{40}{7}x + \frac{520}{7} + 20$
Change $20$ into an equivalent fraction that has $7$ as its denominator so that both fractions have the same denominator:
$y = -\frac{40}{7}x + \frac{520}{7} + \frac{140}{7}$
Add the fractions to simplify:
$y = -\frac{40}{7}x + \frac{660}{7}$
Now, we have the equation of the line in slope-intercept form.
