Question

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

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

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

Step3: Simplify the equation

Expand the right - hand side: \( y - 1=\frac{1}{6}x-1 \). Then add 1 to both sides of the equation: \( y=\frac{1}{6}x \). We can also write it in standard form \( x - 6y = 0 \), but the slope - intercept form \( y=\frac{1}{6}x \) is also a valid equation of the line.

Answer:

The equation of the line is \( y=\frac{1}{6}x \) (or \( x - 6y = 0 \))