Question

a line passes through the points (-5, 7) and (5, 5). 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

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, \( x_1 = -5 \), \( y_1 = 7 \), \( x_2 = 5 \), \( y_2 = 5 \). So \( m = \frac{5 - 7}{5 - (-5)} = \frac{-2}{10} = -\frac{1}{5} \).

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 \( (5, 5) \). Substitute \( m = -\frac{1}{5} \), \( x_1 = 5 \), \( y_1 = 5 \) into the point - slope form: \( y - 5 = -\frac{1}{5}(x - 5) \).

Step3: Convert to slope - intercept form (\( y=mx + b \))

First, distribute the \( -\frac{1}{5} \) on the right - hand side: \( y - 5 = -\frac{1}{5}x+1 \). Then, add 5 to both sides of the equation: \( y=-\frac{1}{5}x + 1+5 \), so \( y = -\frac{1}{5}x+6 \).

Answer:

\( y = -\frac{1}{5}x + 6 \)