SOLUTION: can you help me write an equation of the line having the following properties. is parallel to the graph of (5/4)x-3 and passes through the origin?

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Question 113965This question is from textbook Algebra 1 Applications Connections
: can you help me write an equation of the line having the following properties.






is parallel to the graph of (5/4)x-3 and passes through the origin? This question is from textbook Algebra 1 Applications Connections

Found 3 solutions by stanbon, checkley71, MathLover1:
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
write an equation of the line having the following properties. is parallel to the graph of (5/4)x-3 and passes through the origin?
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The y-intercept is 0; The slope must be 5/4
EQUATION:
y = (5/4)x is parallel to y = (5/4)x-3 and passes thru the origin.
graph%28400%2C300%2C-10%2C10%2C-10%2C10%2C%285%2F4%29x%2C%285%2F4%29x-3%29
================
Cheers,
Stan H.

Answer by checkley71(8403) About Me  (Show Source):
You can put this solution on YOUR website!
the origin has the coordinates of (0,0)
thus the equation with a slope of (5/4) & passing through the origin is:
y=5/4x+0
+graph%28+300%2C+200%2C+-6%2C+5%2C+-10%2C+10%2C+y+=+5x%2F4+%29+ (graph 300x200 pixels, x from -6 to 5, y from -10 to 10, y = 5x/4 ).

Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
Let our equation of the lines be y%5B1%5D+=+m%5B1%5Dx+%2B+b, and y%5B2%5D+=+m%5B2%5Dx+%2B+b,
Given:
parallel to the graph of y%5B1%5D=%285%2F4%29+x-3
If passes through the origin, passes through the (x,y) =(0,0)

So we have:
Using the slope-intercept form, y+=+mx+%2B+b, where m=slope and b=y-intercept,
If the slopes for our lines are m%5B1%5D( for given line) and m%5B2%5D (for line we are looking for), then
we see that the slope m%5B1%5D++ for given line is 5%2F4 and y-intercept is -3
we also know that if slopes are the same, the lines are parallel: m%5B1%5D+=+m%5B2%5D
so slope m%5B2%5D+=5%2F4+ too
since the line passes through the origin, passes through the (x,y) =(0,0), then y-intercept+=+0, or b=0,
the slope-intercept form of our line will be:
y%5B2%5D+=+%285%2F4%29+x
here is the graph:

Solved by pluggable solver: Solve the System of Equations by Graphing



Start with the given system of equations:


125x%2By=-3

125x%2By=0





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


125x%2By=-3 Start with the given equation



1y=-3-125x Subtract 125+x from both sides



1y=-125x-3 Rearrange the equation



y=%28-125x-3%29%2F%281%29 Divide both sides by 1



y=%28-125%2F1%29x%2B%28-3%29%2F%281%29 Break up the fraction



y=-125x-3 Reduce



Now lets graph y=-125x-3 (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+-125x-3%29+ Graph of y=-125x-3




So let's solve for y on the second equation


125x%2By=0 Start with the given equation



1y=0-125x Subtract 125+x from both sides



1y=-125x%2B0 Rearrange the equation



y=%28-125x%2B0%29%2F%281%29 Divide both sides by 1



y=%28-125%2F1%29x%2B%280%29%2F%281%29 Break up the fraction



y=-125x%2B0 Reduce





Now lets add the graph of y=-125x%2B0 to our first plot to get:


+graph%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+10%2C+-125x-3%2C-125x%2B0%29+ Graph of y=-125x-3(red) and y=-125x%2B0(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.