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: Find the y - intercept

Use the point - slope form $y - y_1=m(x - x_1)$ and then convert to slope - intercept form $y=mx + b$. Let's use the point $(3,-7)$ and $m=-2$. $y-(-7)=-2(x - 3)$ $y + 7=-2x+6$ $y=-2x+6 - 7$ $y=-2x - 1$.

Step3: Graph the line

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

Answer:

The equation of the line is $y=-2x - 1$. To graph, plot $(3,-7)$ and $(-3,5)$ and draw a line through them.