SOLUTION: Graph the lineae equation x-4y=8 by using the intercepts.

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Question 417445: Graph the lineae equation x-4y=8 by using the intercepts.
Found 2 solutions by ewatrrr, MathLover1:
Answer by ewatrrr(24785) About Me  (Show Source):
You can put this solution on YOUR website!


Hi

Graphing this linear equation using the intercepts.

 x-4y = 8  |when x=0 then y= -2 AND when y=0 then x = 8

Pt(0,-2) and Pt(8,0) on the line.  Plot Points and connect with a line

Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

Graph the line equation x-4y=8 by using the intercepts
the x-intercept is
x-4%2A0=8
x=8
the y-intercept is
0-4y=8
-4y=8
y=8%2F-4
y=+-2

Solved by pluggable solver: Finding the Equation of a Line
First lets find the slope through the points (8,0) and (0,-2)


m=%28y%5B2%5D-y%5B1%5D%29%2F%28x%5B2%5D-x%5B1%5D%29 Start with the slope formula (note: (x%5B1%5D,y%5B1%5D) is the first point (8,0) and (x%5B2%5D,y%5B2%5D) is the second point (0,-2))


m=%28-2-0%29%2F%280-8%29 Plug in y%5B2%5D=-2,y%5B1%5D=0,x%5B2%5D=0,x%5B1%5D=8 (these are the coordinates of given points)


m=+-2%2F-8 Subtract the terms in the numerator -2-0 to get -2. Subtract the terms in the denominator 0-8 to get -8




m=1%2F4 Reduce



So the slope is

m=1%2F4





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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 (x%5B1%5D,y%5B1%5D) is one of the given points


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


y-0=%281%2F4%29%28x-8%29 Plug in m=1%2F4, x%5B1%5D=8, and y%5B1%5D=0 (these values are given)



y-0=%281%2F4%29x%2B%281%2F4%29%28-8%29 Distribute 1%2F4


y-0=%281%2F4%29x-2 Multiply 1%2F4 and -8 to get -8%2F4. Now reduce -8%2F4 to get -2

y=%281%2F4%29x-2%2B0 Add 0 to both sides to isolate y


y=%281%2F4%29x-2 Combine like terms -2 and 0 to get -2

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Answer:



So the equation of the line which goes through the points (8,0) and (0,-2) is:y=%281%2F4%29x-2


The equation is now in y=mx%2Bb form (which is slope-intercept form) where the slope is m=1%2F4 and the y-intercept is b=-2


Notice if we graph the equation y=%281%2F4%29x-2 and plot the points (8,0) and (0,-2), we get this: (note: if you need help with graphing, check out this solver)


Graph of y=%281%2F4%29x-2 through the points (8,0) and (0,-2)


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