Question

a line passes through the points (2, -2) and (3, -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, \((x_1, y_1)=(2, - 2)\) and \((x_2, y_2)=(3, - 9)\). So, \( m=\frac{-9-(-2)}{3 - 2}=\frac{-9 + 2}{1}=\frac{-7}{1}=-7 \).

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 \((2,-2)\) and \( m=-7 \). Substituting these values, we get \( y-(-2)=-7(x - 2) \). Simplify this equation: \( y + 2=-7x+14 \).

Step3: Convert to slope - intercept form

Subtract 2 from both sides of the equation \( y + 2=-7x + 14 \) to get \( y=-7x+14 - 2 \), which simplifies to \( y=-7x + 12 \).

Answer:

\( y=-7x + 12 \)