SOLUTION: Find the equation, in slope-intercept form, of the line that passes through the points (5, 2) and (-7, 3). Write the equation in slope-intercept form.

Algebra ->  Linear-equations -> SOLUTION: Find the equation, in slope-intercept form, of the line that passes through the points (5, 2) and (-7, 3). Write the equation in slope-intercept form.       Log On


   

Question 170564: Find the equation, in slope-intercept form, of the line that passes through the points (5, 2) and (-7, 3). Write the equation in slope-intercept form.

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=%283-2%29%2F%28-7-5%29 Plug in y%5B2%5D=3, y%5B1%5D=2, x%5B2%5D=-7, and x%5B1%5D=5


m=%281%29%2F%28-7-5%29 Subtract 2 from 3 to get 1


m=%281%29%2F%28-12%29 Subtract 5 from -7 to get -12


m=-1%2F12 Reduce


So the slope of the line that goes through the points and is m=-1%2F12


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-2=%28-1%2F12%29%28x-5%29 Plug in m=-1%2F12, x%5B1%5D=5, and y%5B1%5D=2


y-2=%28-1%2F12%29x%2B%28-1%2F12%29%28-5%29 Distribute


y-2=%28-1%2F12%29x%2B5%2F12 Multiply


y=%28-1%2F12%29x%2B5%2F12%2B2 Add 2 to both sides.


y=%28-1%2F12%29x%2B29%2F12 Combine like terms. note: If you need help with fractions, check out this solver.


y=%28-1%2F12%29x%2B29%2F12 Simplify


So the equation that goes through the points and is y=%28-1%2F12%29x%2B29%2F12