SOLUTION: The question was Use point-slope form to write the equation of the line passing through the two given points. Write each equation in slope-intercept form: P(4,0), Q(6,-8)

Algebra ->  Rectangles -> SOLUTION: The question was Use point-slope form to write the equation of the line passing through the two given points. Write each equation in slope-intercept form: P(4,0), Q(6,-8)      Log On


   

Question 330413: The question was Use point-slope form to write the equation of the line passing through the two given points. Write each equation in slope-intercept form:
P(4,0), Q(6,-8)
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

First let's find the slope of the line through the points and


Note: is the first point . So this means that x%5B1%5D=4 and y%5B1%5D=0.
Also, is the second point . So this means that x%5B2%5D=6 and y%5B2%5D=-8.


m=%28y%5B2%5D-y%5B1%5D%29%2F%28x%5B2%5D-x%5B1%5D%29 Start with the slope formula.


m=%28-8-0%29%2F%286-4%29 Plug in y%5B2%5D=-8, y%5B1%5D=0, x%5B2%5D=6, and x%5B1%5D=4


m=%28-8%29%2F%286-4%29 Subtract 0 from -8 to get -8


m=%28-8%29%2F%282%29 Subtract 4 from 6 to get 2


m=-4 Reduce


So the slope of the line that goes through the points and is m=-4


Now let's use the point slope formula:


y-y%5B1%5D=m%28x-x%5B1%5D%29 Start with the point slope formula


y-0=-4%28x-4%29 Plug in m=-4, x%5B1%5D=4, and y%5B1%5D=0


y-0=-4x%2B-4%28-4%29 Distribute


y-0=-4x%2B16 Multiply


y=-4x%2B16 Simplify


So the equation that goes through the points and is y=-4x%2B16


Notice how the graph of y=-4x%2B16 goes through the points and . So this visually verifies our answer.
Graph of y=-4x%2B16 through the points and