Question

find the equation of the line passing through the points (5,21) and (-5,-29). y = ?x +

Explanation:

Step1: Calculate the slope (m)

The formula for the slope \( m \) between two points \((x_1, y_1)\) and \((x_2, y_2)\) is \( m=\frac{y_2 - y_1}{x_2 - x_1} \).
Given points \((5, 21)\) and \((-5, -29)\), let \( x_1 = 5, y_1 = 21, x_2=-5, y_2 = -29 \).
\[
m=\frac{-29 - 21}{-5 - 5}=\frac{-50}{-10}=5
\]

Step2: Find the y - intercept (b)

We use the point - slope form \( y - y_1=m(x - x_1) \) and substitute \( m = 5 \), \( x_1 = 5 \), \( y_1 = 21 \).
\[
y-21 = 5(x - 5)
\]
Expand the right - hand side: \( y-21=5x-25 \)
Add 21 to both sides: \( y=5x-25 + 21 \)
\[
y=5x-4
\]

Answer:

\( y = 5x-4 \)