SOLUTION: Find an equation of the line containing the given pair of points (1/4, -1/2) and (3/4, 6)

Algebra ->  Linear-equations -> SOLUTION: Find an equation of the line containing the given pair of points (1/4, -1/2) and (3/4, 6)      Log On


   

Question 146603: Find an equation of the line containing the given pair of points
(1/4, -1/2) and (3/4, 6)
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

First let's find the slope 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=%286--1%2F2%29%2F%283%2F4-1%2F4%29 Plug in y%5B2%5D=6, y%5B1%5D=-1%2F2, x%5B2%5D=3%2F4, x%5B1%5D=1%2F4, ,


m=%2813%2F2%29%2F%283%2F4-1%2F4%29 Subtract -1%2F2 from 6 to get 13%2F2


m=%2813%2F2%29%2F%281%2F2%29 Subtract 1%2F4 from 3%2F4 to get 1%2F2


m=%2813%2F2%29%2A%282%2F1%29 Multiply the first fraction by the reciprocal of the second fraction.


m=13 Multiply and reduce.


So the slope of the line that goes through the points and is m=13


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--1%2F2=13%28x-1%2F4%29 Plug in m=13, x%5B1%5D=1%2F4, and y%5B1%5D=-1%2F2


y%2B1%2F2=13%28x-1%2F4%29 Rewrite y--1%2F2 as y%2B1%2F2


y%2B1%2F2=13x%2B13%28-1%2F4%29 Distribute


y%2B1%2F2=13x-13%2F4 Multiply


y=13x-13%2F4-1%2F2 Subtract 1%2F2 from both sides.


y=13x-15%2F4 Combine like terms. note: If you need help with fractions, check out this solver.


y=13x-15%2F4 Simplify


So the equation that goes through the points and is y=13x-15%2F4


Notice how the graph of y=13x-15%2F4 goes through the points and . So this visually verifies our answer.
Graph of y=13x-15%2F4 through the points and