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?

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)   (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.

================
Cheers,
Stan H.
Answer by checkley71(8403)   (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 300x200 pixels, x from -6 to 5, y from -10 to 10, y = 5x/4 ).
Answer by MathLover1(20850)   (Show Source): You can put this solution on YOUR website!
Let our equation of the lines be , and ,
Given:
parallel to the graph of
If passes through the origin, passes through the (,) =(,)

So we have:
Using the slope-intercept form, , where and ,
If the slopes for our lines are ( for given line) and (for line we are looking for), then
we see that the slope for given line is and is
we also know that if slopes are the same, the lines are parallel:
so slope too
since the line passes through the origin, passes through the (,) =(,), then , or ,
the slope-intercept form of our line will be:

here is the graph:

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

Start with the given system of equations:

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

Start with the given equation

Subtract from both sides

Rearrange the equation

Divide both sides by

Break up the fraction

Reduce

Now lets graph (note: if you need help with graphing, check out this solver)

Graph of

So let's solve for y on the second equation

Start with the given equation

Subtract from both sides

Rearrange the equation

Divide both sides by

Break up the fraction

Reduce

Now lets add the graph of to our first plot to get:

Graph of (red) and (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.

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