Question

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

Step2: Use point - slope form to find the equation

The point - slope form is \( y - y_1=m(x - x_1) \). Using the point \((-2,-2)\) and \( m =-\frac{7}{3} \), we have \( y-(-2)=-\frac{7}{3}(x - (-2)) \), which simplifies to \( y + 2=-\frac{7}{3}(x + 2) \).

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

Expand the right - hand side: \( y+2=-\frac{7}{3}x-\frac{14}{3} \). Subtract 2 from both sides. Since \( 2=\frac{6}{3} \), we get \( y=-\frac{7}{3}x-\frac{14}{3}-\frac{6}{3}=-\frac{7}{3}x-\frac{20}{3} \).

Answer:

\( y =-\frac{7}{3}x-\frac{20}{3} \)