Question

a line passes through the points (-13, -8) and (5, 1). 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 \(m=\frac{y_2 - y_1}{x_2 - x_1}\).
Given points \((-13, -8)\) and \((5, 1)\), so \(x_1=-13\), \(y_1 = - 8\), \(x_2 = 5\), \(y_2=1\).
\(m=\frac{1-(-8)}{5-(-13)}=\frac{1 + 8}{5 + 13}=\frac{9}{18}=\frac{1}{2}\)

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 \((5,1)\) and \(m=\frac{1}{2}\).
\(y - 1=\frac{1}{2}(x - 5)\)

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

Expand the right - hand side: \(y-1=\frac{1}{2}x-\frac{5}{2}\)
Add 1 to both sides: \(y=\frac{1}{2}x-\frac{5}{2}+1\)
Simplify the constant term: \(y=\frac{1}{2}x-\frac{5}{2}+\frac{2}{2}=\frac{1}{2}x-\frac{3}{2}\)

Answer:

\(y = \frac{1}{2}x-\frac{3}{2}\)