Question

what is an equation of the line that passes through the points (2, 2) and (4, 8)?

Explanation:

Step1: Calculate the slope

The slope \( m \) between two points \((x_1, y_1)\) and \((x_2, y_2)\) is given by \( m=\frac{y_2 - y_1}{x_2 - x_1} \). For the points \((2,2)\) and \((4,8)\), we have \( x_1 = 2,y_1 = 2,x_2 = 4,y_2 = 8 \). So \( m=\frac{8 - 2}{4 - 2}=\frac{6}{2}=3 \).

Step2: Use point - slope form

The point - slope form of a line is \( y - y_1=m(x - x_1) \). Using the point \((2,2)\) and \( m = 3 \), we get \( y - 2=3(x - 2) \).

Step3: Simplify to slope - intercept form

Expand the right - hand side: \( y - 2=3x-6 \). Then add 2 to both sides: \( y=3x - 6 + 2=3x-4 \).

Answer:

\( y = 3x-4 \) (or other equivalent forms like \( 3x-y=4 \))