Question

a line passes through the points (4, -8) and (6, -9). 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, \( x_1 = 4,y_1=-8,x_2 = 6,y_2=-9 \). So \( m=\frac{-9-(-8)}{6 - 4}=\frac{-9 + 8}{2}=\frac{-1}{2} \).

Step2: Use point - slope form to find the equation

The point - slope form is \( y - y_1=m(x - x_1) \). Using the point \((4,-8)\) and \( m =-\frac{1}{2} \), we have \( y-(-8)=-\frac{1}{2}(x - 4) \). Simplify this: \( y + 8=-\frac{1}{2}x+2 \).

Step3: Solve for y

Subtract 8 from both sides: \( y=-\frac{1}{2}x+2 - 8 \), so \( y=-\frac{1}{2}x-6 \).

Answer:

\( y =-\frac{1}{2}x-6 \)