SOLUTION: write the slope-intercept form of the equation of the line through the given points. through (3,4)and (-2,-5)

Algebra ->  Linear-equations -> SOLUTION: write the slope-intercept form of the equation of the line through the given points. through (3,4)and (-2,-5)       Log On


   

Question 550318: write the slope-intercept form of the equation of the line through the given points.
through (3,4)and (-2,-5)
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=3 and y%5B1%5D=4.
Also, is the second point . So this means that x%5B2%5D=-2 and y%5B2%5D=-5.


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


m=%28-5-4%29%2F%28-2-3%29 Plug in y%5B2%5D=-5, y%5B1%5D=4, x%5B2%5D=-2, and x%5B1%5D=3


m=%28-9%29%2F%28-2-3%29 Subtract 4 from -5 to get -9


m=%28-9%29%2F%28-5%29 Subtract 3 from -2 to get -5


m=9%2F5 Reduce


So the slope of the line that goes through the points and is m=9%2F5


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=%289%2F5%29%28x-3%29 Plug in m=9%2F5, x%5B1%5D=3, and y%5B1%5D=4


y-4=%289%2F5%29x%2B%289%2F5%29%28-3%29 Distribute


y-4=%289%2F5%29x-27%2F5 Multiply


y=%289%2F5%29x-27%2F5%2B4 Add 4 to both sides.


y=%289%2F5%29x-7%2F5 Combine like terms. note: If you need help with fractions, check out this solver.


So the equation that goes through the points and is y=%289%2F5%29x-7%2F5