SOLUTION: What is the equation in slope intercept form of the line that passes through (5,-7) and (2,1)? What is the equation in standard form that passes through the point (-2,6) and has

Algebra ->  Linear-equations -> SOLUTION: What is the equation in slope intercept form of the line that passes through (5,-7) and (2,1)? What is the equation in standard form that passes through the point (-2,6) and has      Log On


   

Question 173208: What is the equation in slope intercept form of the line that passes through (5,-7) and (2,1)?
What is the equation in standard form that passes through the point (-2,6) and has a slope of 4?
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
# 1

Problem:

What is the equation in slope intercept form of the line that passes through (5,-7) and (2,1)?



Solution:




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=%281--7%29%2F%282-5%29 Plug in y%5B2%5D=1, y%5B1%5D=-7, x%5B2%5D=2, and x%5B1%5D=5


m=%288%29%2F%282-5%29 Subtract -7 from 1 to get 8


m=%288%29%2F%28-3%29 Subtract 5 from 2 to get -3


m=-8%2F3 Reduce


So the slope of the line that goes through the points and is m=-8%2F3


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--7=%28-8%2F3%29%28x-5%29 Plug in m=-8%2F3, x%5B1%5D=5, and y%5B1%5D=-7


y%2B7=%28-8%2F3%29%28x-5%29 Rewrite y--7 as y%2B7


y%2B7=%28-8%2F3%29x%2B%28-8%2F3%29%28-5%29 Distribute


y%2B7=%28-8%2F3%29x%2B40%2F3 Multiply


y=%28-8%2F3%29x%2B40%2F3-7 Subtract 7 from both sides.


y=%28-8%2F3%29x%2B19%2F3 Combine like terms. note: If you need help with fractions, check out this solver.


y=%28-8%2F3%29x%2B19%2F3 Simplify


So the equation that goes through the points and is y=%28-8%2F3%29x%2B19%2F3






# 2


Problem:


What is the equation in standard form that passes through the point (-2,6) and has a slope of 4




Solution:




If you want to find the equation of line with a given a slope of 4 which goes through the point (-2,6), you can simply use the point-slope formula to find the equation:


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

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


y-6=%284%29%28x--2%29 Plug in m=4, x%5B1%5D=-2, and y%5B1%5D=6 (these values are given)


y-6=%284%29%28x%2B2%29 Rewrite x--2 as x%2B2


y-6=4x%2B%284%29%282%29 Distribute 4


y-6=4x%2B8 Multiply 4 and 2 to get 8


y-6-4x=8 Subtract 4x from both sides.


y-4x=8%2B6 Add 6 to both sides.


-4x%2By=14 Combine like terms.


4x-y=-14 Multiply EVERY term by -1 to make the "x" coefficient positive.

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

Answer:


So the equation in standard form that has a slope of 4 and passes through the point (-2,6) is


4x-y=-14