Question

graph the line that passes through the points (3, -7) and (-3, 5) and determine the equation of the line.

Explanation:

Step1: Calculate the slope

The slope formula is $m=\frac{y_2 - y_1}{x_2 - x_1}$. Let $(x_1,y_1)=(3,-7)$ and $(x_2,y_2)=(-3,5)$. Then $m=\frac{5 - (-7)}{-3 - 3}=\frac{5 + 7}{-6}=\frac{12}{-6}=-2$.

Step2: Use the point - slope form

The point - slope form of a line is $y - y_1=m(x - x_1)$. Using the point $(3,-7)$ and $m = - 2$, we have $y-(-7)=-2(x - 3)$.

Step3: Simplify the equation

$y + 7=-2x+6$. Rearranging to the slope - intercept form $y=mx + b$, we get $y=-2x-1$.

Step4: Graph the line

Plot the points $(3,-7)$ and $(-3,5)$ on the coordinate plane. Then draw a straight line passing through them.

Answer:

The equation of the line is $y=-2x - 1$