Question

find an equation of the line containing the given pair of points. (-7, -8) and (-3, -9)
the equation of the line in slope - intercept form is y = . (simplify your answer. use integers or fractions for any numbers in the expression.)

Explanation:

Step1: Calculate the slope

The slope $m$ formula is $m=\frac{y_2 - y_1}{x_2 - x_1}$. Let $(x_1,y_1)=(-7,-8)$ and $(x_2,y_2)=(-3,-9)$. Then $m=\frac{-9-(-8)}{-3-(-7)}=\frac{-9 + 8}{-3 + 7}=\frac{-1}{4}=-\frac{1}{4}$.

Step2: Use point - slope form to find y - intercept

The point - slope form is $y - y_1=m(x - x_1)$. Using the point $(-7,-8)$ and $m =-\frac{1}{4}$, we have $y-(-8)=-\frac{1}{4}(x - (-7))$, which simplifies to $y + 8=-\frac{1}{4}(x + 7)$. Expand the right - hand side: $y+8=-\frac{1}{4}x-\frac{7}{4}$.

Step3: Solve for y

Subtract 8 from both sides. $y=-\frac{1}{4}x-\frac{7}{4}-8$. Since $8=\frac{32}{4}$, then $y=-\frac{1}{4}x-\frac{7 + 32}{4}=-\frac{1}{4}x-\frac{39}{4}$.

Answer:

$y =-\frac{1}{4}x-\frac{39}{4}$