Question

write an equation for the line, in point - slope form, that passes through the following points: (2, 2) (1, 8)

Explanation:

Step1: Calculate the slope

The slope formula is $m = \frac{y_2 - y_1}{x_2 - x_1}$. Let $(x_1, y_1) = (2, 2)$ and $(x_2, y_2) = (1, 8)$. Then $m = \frac{8 - 2}{1 - 2} = \frac{6}{-1} = -6$.

Step2: Use point - slope form

The point - slope form of a line is $y - y_1 = m(x - x_1)$. We can use the point $(2, 2)$ (we could also use $(1, 8)$). Substitute $m=-6$, $x_1 = 2$, and $y_1 = 2$ into the formula: $y - 2=-6(x - 2)$. We could also use the point $(1,8)$: $y - 8=-6(x - 1)$.

Answer:

$y - 2=-6(x - 2)$ (or $y - 8=-6(x - 1)$)