Question

a line passes through the points (-7, 0) and (7, -2). write its equation in slope - intercept form. write your answer using integers, proper fractions, and improper fractions in simplest form.

Explanation:

Step1: Calculate the slope (m)

The formula for slope between two points \((x_1, y_1)\) and \((x_2, y_2)\) is \(m = \frac{y_2 - y_1}{x_2 - x_1}\).
Here, \(x_1=-7\), \(y_1 = 0\), \(x_2 = 7\), \(y_2=-2\).
So, \(m=\frac{-2 - 0}{7 - (-7)}=\frac{-2}{14}=-\frac{1}{7}\).

Step2: Use point - slope form to find the equation

The point - slope form is \(y - y_1=m(x - x_1)\). Let's use the point \((-7,0)\).
Substitute \(m = -\frac{1}{7}\), \(x_1=-7\), \(y_1 = 0\) into the formula:
\(y-0=-\frac{1}{7}(x - (-7))\)
Simplify the right - hand side: \(y=-\frac{1}{7}(x + 7)\)
Expand the right - hand side: \(y=-\frac{1}{7}x-1\)

Answer:

\(y = -\frac{1}{7}x - 1\)