SOLUTION: Find the slope of any line parallel to the line through points (15,1) and (4,2). Thanks for your help.

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Question 117941: Find the slope of any line parallel to the line through points (15,1) and (4,2). Thanks for your help.
Found 2 solutions by misscrt, MathLover1:
Answer by misscrt(37) About Me  (Show Source):
You can put this solution on YOUR website!
Find the slope of any line parallel to the line through points (15,1) and (4,2). Thanks for your help.
First find the slope of the line. The slopes will be the same because the lines are parallel.
So,
m=(y2-y1)/(x2-x1)
=(2-1)/(4-15)
=1/-11
= - 1/11
Hope that helps.
Greetings,
misscrt

Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
first find equation of the line through points (15,1) and (4,2)in slope-intercept form
Solved by pluggable solver: FIND EQUATION of straight line given 2 points
hahaWe are trying to find equation of form y=ax+b, where a is slope, and b is intercept, which passes through points (x1, y1) = (15, 1) and (x2, y2) = (4, 2).
Slope a is .
Intercept is found from equation a%2Ax%5B1%5D%2Bb+=+y%5B1%5D, or -0.0909090909090909%2A15+%2Bb+=+2.36363636363636. From that,
intercept b is b=y%5B1%5D-a%2Ax%5B1%5D, or b=1--0.0909090909090909%2A15+=+2.36363636363636.

y=(-0.0909090909090909)x + (2.36363636363636)

Your graph:





the slope of any line parallel to this line with slope a=0.09 will be a%5B1%5D=0.09 because parallel lines have equal+slopes
proof:
if we take y%5B1%5D=0.9+%2B+6 as the line parallel to the line through given points, then we have :
Solved by pluggable solver: Solve the System of Equations by Graphing



Start with the given system of equations:


09x%2By=236

09x%2By=6





In order to graph these equations, we need to solve for y for each equation.




So let's solve for y on the first equation


09x%2By=236 Start with the given equation



1y=236-09x Subtract 09+x from both sides



1y=-09x%2B236 Rearrange the equation



y=%28-09x%2B236%29%2F%281%29 Divide both sides by 1



y=%28-09%2F1%29x%2B%28236%29%2F%281%29 Break up the fraction



y=-9x%2B236 Reduce



Now lets graph y=-9x%2B236 (note: if you need help with graphing, check out this solver)



+graph%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+10%2C+-9x%2B236%29+ Graph of y=-9x%2B236




So let's solve for y on the second equation


09x%2By=6 Start with the given equation



1y=6-09x Subtract 09+x from both sides



1y=-09x%2B6 Rearrange the equation



y=%28-09x%2B6%29%2F%281%29 Divide both sides by 1



y=%28-09%2F1%29x%2B%286%29%2F%281%29 Break up the fraction



y=-9x%2B6 Reduce





Now lets add the graph of y=-9x%2B6 to our first plot to get:


+graph%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+10%2C+-9x%2B236%2C-9x%2B6%29+ Graph of y=-9x%2B236(red) and y=-9x%2B6(green)


From the graph, we can see that the two lines are parallel and will never intersect. So there are no solutions and the system is inconsistent.