Question

1. write an equation in point - slope for the line that passes through the points (2, 3) and (-1, 7).

Explanation:

Step1: Calculate the slope

The slope formula is $m = \frac{y_2 - y_1}{x_2 - x_1}$. Let $(x_1, y_1) = (2, 3)$ and $(x_2, y_2) = (-1, 7)$. Then $m = \frac{7 - 3}{-1 - 2} = \frac{4}{-3} = -\frac{4}{3}$.

Step2: Use point - slope form

The point - slope form of a line is $y - y_1 = m(x - x_1)$. We can use either of the two points. Let's use the point $(2, 3)$ first. Substituting $m = -\frac{4}{3}$, $x_1 = 2$ and $y_1 = 3$ into the point - slope formula, we get $y - 3 = -\frac{4}{3}(x - 2)$. We can also use the point $(-1,7)$. Substituting $m = -\frac{4}{3}$, $x_1=-1$ and $y_1 = 7$ into the formula, we get $y - 7=-\frac{4}{3}(x + 1)$ (since $x-(-1)=x + 1$).

Answer:

$y - 3 = -\frac{4}{3}(x - 2)$ or $y - 7=-\frac{4}{3}(x + 1)$