Question

find an equation of the line that passes through the two given points. write the equation. passes through (1, 8) and (-2, -1)

Explanation:

Step1: Find the slope

The formula for 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 \((1, 8)\) and \((-2, -1)\), so \( x_1 = 1, y_1 = 8, x_2=-2, y_2=-1 \).
\( m=\frac{-1 - 8}{-2 - 1}=\frac{-9}{-3}=3 \)

Step2: Use point - slope form

The point - slope form of a line is \( y - y_1=m(x - x_1) \). Let's use the point \((1, 8)\) and \( m = 3 \).
Substitute into the formula: \( y - 8=3(x - 1) \)

Step3: Simplify to slope - intercept form

Expand the right - hand side: \( y - 8 = 3x-3 \)
Add 8 to both sides: \( y=3x - 3 + 8 \)
\( y=3x + 5 \)
We can also write it in standard form \( 3x-y=-5 \)

Answer:

The equation of the line is \( y = 3x+5 \) (or \( 3x - y=-5 \))