Question

what is an equation of the line that passes through the points (6, 3) and (-6, 1)?

Explanation:

Step1: Find the slope (m)

The formula for slope \( m \) between two points \( (x_1, y_1) \) and \( (x_2, y_2) \) is \( m=\frac{y_2 - y_1}{x_2 - x_1} \).
Substituting \( (x_1, y_1)=(6, 3) \) and \( (x_2, y_2)=(- 6, 1) \), we get:
\( m=\frac{1 - 3}{-6 - 6}=\frac{-2}{-12}=\frac{1}{6} \)

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 \( (6, 3) \) (we could also use \( (-6,1) \)).
Substitute \( m = \frac{1}{6} \), \( x_1 = 6 \) and \( y_1 = 3 \) into the point - slope form:
\( y-3=\frac{1}{6}(x - 6) \)
Expand the right - hand side: \( y-3=\frac{1}{6}x-1 \)
Add 3 to both sides: \( y=\frac{1}{6}x+2 \)
We can also write it in standard form \( Ax + By=C \). Multiply through by 6 to get \( x-6y=-12 \) (or keep it in slope - intercept form \( y=\frac{1}{6}x + 2 \))

Answer:

\( y=\frac{1}{6}x + 2 \) (or \( x-6y=-12 \))