Question

what is an equation of the line that passes through the points (-6, 1) and (6, 7)?

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, \( x_1=-6,y_1 = 1,x_2=6,y_2 = 7 \). So \( m=\frac{7 - 1}{6-(-6)}=\frac{6}{12}=\frac{1}{2} \).

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 \((-6,1)\). Substitute \( m=\frac{1}{2},x_1=-6,y_1 = 1 \) into the formula: \( y - 1=\frac{1}{2}(x+6) \).

Step3: Convert to slope - intercept form

Expand the right - hand side: \( y - 1=\frac{1}{2}x + 3 \). Then add 1 to both sides: \( y=\frac{1}{2}x+4 \). We can also write it in standard form \( x-2y=-8 \), but the slope - intercept form is also a valid equation of the line.

Answer:

\( y=\frac{1}{2}x + 4 \) (or equivalent forms like \( x-2y=-8 \) or \( y - 7=\frac{1}{2}(x - 6) \))