Question

use the information given to write linear equations in all forms.

1. a line that passes through points (8, 2) and (2, -10).

find the slope: m =
point - slope:
slope - intercept:
standard:

Explanation:

Step1: Calculate the slope

The formula for slope \( m \) between two points \((x_1, y_1)\) and \((x_2, y_2)\) is \( m=\frac{y_2 - y_1}{x_2 - x_1} \). Here, \((x_1, y_1)=(8, 2)\) and \((x_2, y_2)=(2, - 10)\). So \( m=\frac{-10 - 2}{2 - 8}=\frac{-12}{-6} = 2 \).

Step2: Point - Slope form

The point - slope form of a line is \( y - y_1=m(x - x_1) \). Using the point \((8, 2)\) and \( m = 2 \), we get \( y - 2=2(x - 8) \).

Step3: Slope - intercept form

Start with the point - slope form \( y - 2=2(x - 8) \). Expand the right - hand side: \( y - 2=2x-16 \). Then add 2 to both sides: \( y=2x - 14 \).

Step4: Standard form

The standard form of a line is \( Ax+By = C \) (where \( A\), \( B\), and \( C\) are integers and \( A\geq0 \)). Start with \( y=2x - 14 \). Subtract \( 2x \) from both sides: \( - 2x+y=-14 \). Multiply both sides by - 1 to make \( A = 2\geq0 \): \( 2x - y=14 \).

Answer:

• Slope: \( \boldsymbol{2} \)
• Point - Slope: \( \boldsymbol{y - 2 = 2(x - 8)} \)
• Slope - intercept: \( \boldsymbol{y = 2x-14} \)
• Standard: \( \boldsymbol{2x - y=14} \)