SOLUTION: Write the slope-intercept equation for the line that passes through (5, 4) and (7, 8). Please show all of your work.

Algebra ->  Linear-equations -> SOLUTION: Write the slope-intercept equation for the line that passes through (5, 4) and (7, 8). Please show all of your work.       Log On


   

Question 448626: Write the slope-intercept equation for the line that passes through (5, 4) and (7, 8). Please show all of your work.
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


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


m=%288-4%29%2F%287-5%29 Plug in y%5B2%5D=8, y%5B1%5D=4, x%5B2%5D=7, and x%5B1%5D=5


m=%284%29%2F%287-5%29 Subtract 4 from 8 to get 4


m=%284%29%2F%282%29 Subtract 5 from 7 to get 2


m=2 Reduce


So the slope of the line that goes through the points and is m=2


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-4=2%28x-5%29 Plug in m=2, x%5B1%5D=5, and y%5B1%5D=4


y-4=2x%2B2%28-5%29 Distribute


y-4=2x-10 Multiply


y=2x-10%2B4 Add 4 to both sides.


y=2x-6 Combine like terms.


So the equation that goes through the points and is y=2x-6


Notice how the graph of y=2x-6 goes through the points and . So this visually verifies our answer.
Graph of y=2x-6 through the points and