10. what is the equation in point - slope form of the line that passes through (-7, 1) and (-3, 9)?

Explanation:

Step1: Calculate the slope

The slope formula is $m = \frac{y_2 - y_1}{x_2 - x_1}$. Let $(x_1, y_1) = (-7, 1)$ and $(x_2, y_2) = (-3, 9)$. Then $m = \frac{9 - 1}{-3 - (-7)} = \frac{8}{4} = 2$.

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 $(-7, 1)$ with $m = 2$. Substituting into the formula, we get $y - 1 = 2(x - (-7))$, which simplifies to $y - 1 = 2(x + 7)$. We could also use the point $(-3, 9)$: $y - 9 = 2(x - (-3))$ or $y - 9 = 2(x + 3)$.

Answer:

The equation in point - slope form is $y - 1 = 2(x + 7)$ (or $y - 9 = 2(x + 3)$)