Question

find an equation of the line containing the given pair of points. (-1, -7) and (-3, -4)
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 $m$ 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, $x_1=-1,y_1 = - 7,x_2=-3,y_2=-4$. So $m=\frac{-4-(-7)}{-3-(-1)}=\frac{-4 + 7}{-3 + 1}=\frac{3}{-2}=-\frac{3}{2}$.

Step2: Use the point - slope form

The point - slope form of a line is $y - y_1=m(x - x_1)$. Using the point $(-1,-7)$ and $m =-\frac{3}{2}$, we have $y-(-7)=-\frac{3}{2}(x-(-1))$, which simplifies to $y + 7=-\frac{3}{2}(x + 1)$.

Step3: Convert to slope - intercept form

Expand the right - hand side: $y+7=-\frac{3}{2}x-\frac{3}{2}$. Then subtract 7 from both sides. $y=-\frac{3}{2}x-\frac{3}{2}-7=-\frac{3}{2}x-\frac{3 + 14}{2}=-\frac{3}{2}x-\frac{17}{2}$.

Answer:

$y =-\frac{3}{2}x-\frac{17}{2}$