Question

graph the line that passes through the points (-6, 2) and (6, 4) and determine the equation of the line.

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 \((-6, 2)\) and \((6, 4)\), we have \( x_1=-6,y_1 = 2,x_2=6,y_2 = 4 \). So \( m=\frac{4 - 2}{6-(-6)}=\frac{2}{12}=\frac{1}{6} \).

Step2: Use point - slope form to find the equation

The point - slope form of a line is \( y - y_1=m(x - x_1) \). Let's use the point \((-6,2)\). Substitute \( m = \frac{1}{6}\), \( x_1=-6 \) and \( y_1 = 2 \) into the formula:
\( y - 2=\frac{1}{6}(x+6) \)
Expand the right - hand side: \( y - 2=\frac{1}{6}x + 1 \)
Then, add 2 to both sides: \( y=\frac{1}{6}x+3 \)
(For graphing: Plot the points \((-6,2)\) and \((6,4)\) on the coordinate plane and draw a straight line passing through them.)

Answer:

The equation of the line is \( y=\frac{1}{6}x + 3 \)