Question

1. write the equation of the line in slope-intercept form that passes through (4, -2) and (8, 6).

Explanation:

Step1: Calculate the slope

The slope \( m \) between two points \((x_1, y_1)\) and \((x_2, y_2)\) is given by \( m=\frac{y_2 - y_1}{x_2 - x_1} \). Here, \((x_1,y_1)=(4, - 2)\) and \((x_2,y_2)=(8,6)\). So, \( m=\frac{6-(-2)}{8 - 4}=\frac{8}{4}=2 \).

Step2: Use point - slope form to find the equation

The point - slope form is \( y - y_1=m(x - x_1) \). Using the point \((4,-2)\) and \( m = 2 \), we get \( y-(-2)=2(x - 4) \), which simplifies to \( y + 2=2x-8 \).

Step3: Convert to slope - intercept form (\(y=mx + b\))

Subtract 2 from both sides of the equation \( y + 2=2x-8 \). So, \( y=2x-8 - 2=2x-10 \).

Answer:

\(y = 2x-10\)