SOLUTION: Write an equation in standard form of the line with the given x-intercept and y-intercept. x-intercept -3 y-intercept -5 PLEASE HELP!

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Question 117172: Write an equation in standard form of the line with the given x-intercept and y-intercept.
x-intercept -3
y-intercept -5
PLEASE HELP!
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Since the equation has the x-intercept -3 and the y-intercept -5, this means the equation goes through the points (-3,0) and (0,-5)


First lets find the slope through the points (-3,0) and (0,-5)

m=%28y%5B2%5D-y%5B1%5D%29%2F%28x%5B2%5D-x%5B1%5D%29 Start with the slope formula (note: is the first point (-3,0) and is the second point (0,-5))

m=%28-5-0%29%2F%280--3%29 Plug in y%5B2%5D=-5,y%5B1%5D=0,x%5B2%5D=0,x%5B1%5D=-3 (these are the coordinates of given points)

m=+-5%2F3 Subtract the terms in the numerator -5-0 to get -5. Subtract the terms in the denominator 0--3 to get 3

So the slope is
m=-5%2F3

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Now let's use the point-slope formula to find the equation of the line:



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

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

y-0=%28-5%2F3%29%28x--3%29 Plug in m=-5%2F3, x%5B1%5D=-3, and y%5B1%5D=0 (these values are given)


y-0=%28-5%2F3%29%28x%2B3%29 Rewrite x--3 as x%2B3


y-0=%28-5%2F3%29x%2B%28-5%2F3%29%283%29 Distribute -5%2F3

y-0=%28-5%2F3%29x-5 Multiply -5%2F3 and 3 to get -15%2F3. Now reduce -15%2F3 to get -5

y=%28-5%2F3%29x-5%2B0 Add 0 to both sides to isolate y

y=%28-5%2F3%29x-5 Combine like terms -5 and 0 to get -5
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Answer:


So the equation of the line which goes through the points (-3,0) and (0,-5) is:y=%28-5%2F3%29x-5

The equation is now in y=mx%2Bb form (which is slope-intercept form) where the slope is m=-5%2F3 and the y-intercept is b=-5

Notice if we graph the equation y=%28-5%2F3%29x-5 and plot the points (-3,0) and (0,-5), we get this: (note: if you need help with graphing, check out this solver)

Graph of y=%28-5%2F3%29x-5 through the points (-3,0) and (0,-5)

Notice how the two points lie on the line. This graphically verifies our answer.


Now let's convert the equation into standard form


Solved by pluggable solver: Converting Linear Equations in Standard form to Slope-Intercept Form (and vice versa)
Convert from slope-intercept form (y = mx+b) to standard form (Ax+By = C)


y+=+%28-5%2F3%29x-5 Start with the given equation


3%2Ay+=+3%2A%28%28-5%2F3%29x-5%29 Multiply both sides by the LCD 3


3y+=+-5x-15 Distribute and multiply


3y%2B5x+=+-5x-15%2B5x Add 5x to both sides


5x%2B3y+=+-15 Simplify


The original equation y+=+%28-5%2F3%29x-5 (slope-intercept form) is equivalent to 5x%2B3y+=+-15 (standard form where A > 0)


The equation 5x%2B3y+=+-15 is in the form Ax%2BBy+=+C where A+=+5, B+=+3 and C+=+-15






So the standard equation that x-intercept -3 and the y-intercept -5 is
5x%2B3y=-15