Question

problem 6.2:
write an equation for this line:
y = ____ x + _____
(-2,8)
(3,-2)

Explanation:

Step1: Calculate the slope

The slope \( m \) between two points \((x_1, y_1) = (-2, 8)\) and \((x_2, y_2) = (3, -2)\) is given by \( m=\frac{y_2 - y_1}{x_2 - x_1} \).
Substituting the values: \( m=\frac{-2 - 8}{3 - (-2)}=\frac{-10}{5}=-2 \).

Step2: Use point - slope form to find the equation

We use the point - slope form \( y - y_1=m(x - x_1) \). Let's use the point \((-2,8)\) and \( m = - 2 \).
\( y - 8=-2(x - (-2)) \)
\( y - 8=-2(x + 2) \)
Expand the right - hand side: \( y - 8=-2x-4 \)
Add 8 to both sides: \( y=-2x + 4 \)

Answer:

\( y=-2x + 4 \)