Question

write an equation in point - slope form for a line that passes through the given set of points. (3,5) and (-6,-4)

Explanation:

Step1: Calculate the slope

The slope formula is $m = \frac{y_2 - y_1}{x_2 - x_1}$. Let $(x_1, y_1) = (3, 5)$ and $(x_2, y_2) = (-6, -4)$. Then $m = \frac{-4 - 5}{-6 - 3} = \frac{-9}{-9} = 1$.

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 $(3, 5)$ (we could also use $(-6, -4)$). Substitute $m = 1$, $x_1 = 3$, and $y_1 = 5$ into the formula. We get $y - 5 = 1\times(x - 3)$, which simplifies to $y - 5 = x - 3$. If we use the point $(-6, -4)$, substituting $m = 1$, $x_1=-6$, and $y_1 = - 4$ into the formula gives $y - (-4)=1\times(x - (-6))$, or $y + 4 = x + 6$.

Answer:

Using the point $(3,5)$: $y - 5 = x - 3$; Using the point $(-6,-4)$: $y + 4 = x + 6$ (either form is correct for point - slope form)