Question

write the equation of the line that passes through the points (-8, -9) and (3, -4). put your answer in fully simplified point - slope form, unless it is a vertical or horizontal line.

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, \((x_1,y_1)=(-8,-9)\) and \((x_2,y_2)=(3,-4)\). So, \( m=\frac{-4 - (-9)}{3 - (-8)}=\frac{-4 + 9}{3 + 8}=\frac{5}{11} \).

Step2: Use point - slope form

The point - slope form of a line is \( y - y_1=m(x - x_1) \). We can use either of the two points. Let's use the point \((3,-4)\) (we could also use \((-8,-9)\)). Substituting \( m = \frac{5}{11} \), \( x_1 = 3 \) and \( y_1=-4 \) into the point - slope formula, we get \( y - (-4)=\frac{5}{11}(x - 3) \), which simplifies to \( y + 4=\frac{5}{11}(x - 3) \). If we use the point \((-8,-9)\), substituting \( m=\frac{5}{11} \), \( x_1=-8 \) and \( y_1 = - 9\) into the point - slope formula, we get \( y-(-9)=\frac{5}{11}(x - (-8)) \), which simplifies to \( y + 9=\frac{5}{11}(x + 8) \).

Answer:

\( y + 4=\frac{5}{11}(x - 3) \) (or \( y + 9=\frac{5}{11}(x + 8) \))