Question

write the equation of the line that passes through the points (-1, 3) and (-9, 5). put your answer in fully simplified point - slope form, unless it is a vertical or horizontal line.

Explanation:

Step1: Find 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, \( x_1=-1,y_1 = 3,x_2=-9,y_2 = 5 \). So \( m=\frac{5 - 3}{-9-(-1)}=\frac{2}{-8}=-\frac{1}{4} \).

Step2: Use point - slope form

The point - slope form of a line is \( y - y_1=m(x - x_1) \). We can use the point \((-1,3)\) (we could also use \((-9,5)\)). Substitute \( m = -\frac{1}{4}\), \( x_1=-1\) and \( y_1 = 3 \) into the point - slope formula.
\( y - 3=-\frac{1}{4}(x-(-1)) \), which simplifies to \( y - 3=-\frac{1}{4}(x + 1) \).

Answer:

\( y - 3=-\frac{1}{4}(x + 1) \)