Question

graph the line that passes through the points (-9,7) and (-3,3) and determine the equation of the 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, \((x_1,y_1)=(-9,7)\) and \((x_2,y_2)=(-3,3)\). So, \( m=\frac{3 - 7}{-3-(-9)}=\frac{-4}{6}=-\frac{2}{3} \).

Step2: Use point - slope form

The point - slope form of a line is \( y - y_1=m(x - x_1) \). Let's use the point \((-3,3)\). Substitute \( m = -\frac{2}{3} \), \( x_1=-3 \) and \( y_1 = 3 \) into the formula:
\( y-3=-\frac{2}{3}(x + 3) \)

Step3: Simplify to slope - intercept form

Expand the right - hand side: \( y-3=-\frac{2}{3}x-2 \)
Add 3 to both sides: \( y=-\frac{2}{3}x + 1 \)

To graph the line, plot the points \((-9,7)\) and \((-3,3)\) on the coordinate plane and then draw a straight line passing through them.

Answer:

The equation of the line is \( y = -\frac{2}{3}x+1 \)