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. y =

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, \((x_1, y_1)=(- 13,-8)\) and \((x_2, y_2)=(5,1)\). So \( m=\frac{1-(-8)}{5 - (-13)}=\frac{1 + 8}{5+13}=\frac{9}{18}=\frac{1}{2} \).

Step2: Use point - slope form to find the equation

The point - slope form of a line is \( y - y_1=m(x - x_1) \). We can use the point \((5,1)\) and \( m = \frac{1}{2} \). Substitute into the formula: \( y-1=\frac{1}{2}(x - 5) \).

Step3: Convert to slope - intercept form

Expand the right - hand side: \( y-1=\frac{1}{2}x-\frac{5}{2} \). Then add 1 to both sides. Since \( 1=\frac{2}{2} \), we have \( y=\frac{1}{2}x-\frac{5}{2}+\frac{2}{2}=\frac{1}{2}x-\frac{3}{2} \).

Answer:

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