SOLUTION: how would i write the equation for a pair of parallel lines with the points: (-4,-1), (1,1) [one of them] and (-2,-5), (3,-3) [the other]???

Algebra ->  Linear-equations -> SOLUTION: how would i write the equation for a pair of parallel lines with the points: (-4,-1), (1,1) [one of them] and (-2,-5), (3,-3) [the other]???      Log On


   

Question 59475This question is from textbook
: how would i write the equation for a pair of parallel lines with the points:
(-4,-1), (1,1) [one of them] and (-2,-5), (3,-3) [the other]??? This question is from textbook

Answer by funmath(2933) About Me  (Show Source):
You can put this solution on YOUR website!
how would i write the equation for a pair of parallel lines with the points:
(-4,-1), (1,1) [one of them] and (-2,-5), (3,-3) [the other]???
You're right the lines would be parallel.
The slope of the first line can be found with the slope formula: highlight%28m=%28y2-y1%29%2F%28x2-x1%29%29, where (x1,y1) and (x2,y2) are given points and m is slope.
For (-4,-1) and (1,1) the slope is:
m=%281-%28-1%29%29%2F%281-%28-4%29%29
m=%281%2B1%29%2F%281%2B4%29
m=2%2F5 The slope of the other 2 points is also 2/5. All parallel lines have the same slope.
:
Once you have a slope and a point you can write the equation of a line using the point-slope formula highlight%28y-y1=m%28x-x1%29%29, m=slope, and (x1,y1)=any point on the line:
For the first set of points, let m=2/5 and (x1,y1)=(1,1)
y-1=%282%2F5%29%28x-1%29
5%28y-1%29=5%282%2F5%29%28x-1%29
5y-5=2%28x-1%29
5y-5=2x-2
5y-5%2B5=2x-2%2B5
5y=2x%2B3
5y%2F5=%282%2F5%29x%2B3%2F5
highlight%28y=%282%2F5%29x%2B3%2F5%29
For fun, you can use the other point to get this same equation.
:
I'll let you prove that I'm right about the slope of the other two points is also m=2/5 (x1,y1)=(-2,-5)
y-%28-5%29=%282%2F5%29%28x-%28-2%29%29
y%2B5=%282%2F5%29%28x%2B2%29
5%28y%2B5%29=5%282%2F5%29%28x%2B2%29
5y%2B25=2%28x%2B2%29
5y%2B25=2x%2B4
5y%2B25-25=2x%2B4-25
5y=2x-21
5y%2F5=%282%2F5%29x-21%2F5
highlight%28y=%282%2F5%29x-21%2F5%29
Now use the other point to get this same equation for fun.
Happy Calculating!!!