SOLUTION: Hello:) Please help me with this question: Find the equation of the line through the given pair of points in standard form using only integers (-4, 3) and (5,6) Thank You!

Algebra ->  Graphs -> SOLUTION: Hello:) Please help me with this question: Find the equation of the line through the given pair of points in standard form using only integers (-4, 3) and (5,6) Thank You!      Log On


   

Question 133009: Hello:)
Please help me with this question: Find the equation of the line through the given pair of points in standard form using only integers
(-4, 3) and (5,6)
Thank You!
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
First lets find the slope through the points (-4,3) and (5,6)

m=%28y%5B2%5D-y%5B1%5D%29%2F%28x%5B2%5D-x%5B1%5D%29 Start with the slope formula (note: is the first point (-4,3) and is the second point (5,6))

m=%286-3%29%2F%285--4%29 Plug in y%5B2%5D=6,y%5B1%5D=3,x%5B2%5D=5,x%5B1%5D=-4 (these are the coordinates of given points)

m=+3%2F9 Subtract the terms in the numerator 6-3 to get 3. Subtract the terms in the denominator 5--4 to get 9


m=1%2F3 Reduce

So the slope is
m=1%2F3

------------------------------------------------


Now let's use the point-slope formula to find the equation of the line:



------Point-Slope Formula------
y-y%5B1%5D=m%28x-x%5B1%5D%29 where m is the slope, and is one of the given points

So lets use the Point-Slope Formula to find the equation of the line

y-3=%281%2F3%29%28x--4%29 Plug in m=1%2F3, x%5B1%5D=-4, and y%5B1%5D=3 (these values are given)


y-3=%281%2F3%29%28x%2B4%29 Rewrite x--4 as x%2B4


y-3=%281%2F3%29x%2B%281%2F3%29%284%29 Distribute 1%2F3

y-3=%281%2F3%29x%2B4%2F3 Multiply 1%2F3 and 4 to get 4%2F3

y=%281%2F3%29x%2B4%2F3%2B3 Add 3 to both sides to isolate y

y=%281%2F3%29x%2B13%2F3 Combine like terms 4%2F3 and 3 to get 13%2F3 (note: if you need help with combining fractions, check out this solver)





So the equation of the line which goes through the points (-4,3) and (5,6) is:


y=%281%2F3%29x%2B13%2F3 (note: this equation is in slope intercept form)


So lets convert it into standard form:


3y=x%2B13 Multiply both sides by 3 to clear the fractions


3y-x=13 Subtract x from both sides


-x%2B3y=13 Rearrange the equation



So the equation in standard form that goes through the points (-4,3) and (5,6) is


-x%2B3y=13