graph the line that passes through the points (8, -4) and (-8, 8) and determine the equation of the line.
graph the line that passes through the points (8, -4) and (-8, 8) and determine the equation of the line.
Answer
Explanation:
Step1: Calculate the slope
The slope $m$ formula is $m=\frac{y_2 - y_1}{x_2 - x_1}$. Let $(x_1,y_1)=(8,-4)$ and $(x_2,y_2)=(-8,8)$. Then $m=\frac{8 - (-4)}{-8 - 8}=\frac{12}{-16}=-\frac{3}{4}$.
Step2: Find the y - intercept
Use the point - slope form $y - y_1=m(x - x_1)$ and then convert to slope - intercept form $y=mx + b$. Using the point $(8,-4)$ and $m =-\frac{3}{4}$, we have $y+4=-\frac{3}{4}(x - 8)$. Expand: $y+4=-\frac{3}{4}x+6$. Then $y=-\frac{3}{4}x + 2$.
To graph, plot the two points $(8,-4)$ and $(-8,8)$ and draw a straight line through them.
Answer:
The equation of the line is $y =-\frac{3}{4}x+2$