SOLUTION: I need to write an equation for the line described in slow intercept form. x - intercept -2 , y intercept 4

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Question 78373: I need to write an equation for the line described in slow intercept form.

x - intercept -2 , y intercept 4
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Since we know the x and y intercept, we can treat these as two points on our line. So to find the equation of the line through these two points, we need to find the slope first.
So we have the x-intercept of (-2,0) and the y-intercept of (0,4) and so these are our two points. Now lets find the slope:

Solved by pluggable solver: Finding the Equation of a Line
First lets find the slope through the points (-2,0) and (0,4)


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 (-2,0) and (x%5B2%5D,y%5B2%5D) is the second point (0,4))


m=%284-0%29%2F%280--2%29 Plug in y%5B2%5D=4,y%5B1%5D=0,x%5B2%5D=0,x%5B1%5D=-2 (these are the coordinates of given points)


m=+4%2F2 Subtract the terms in the numerator 4-0 to get 4. Subtract the terms in the denominator 0--2 to get 2




m=2 Reduce



So the slope is

m=2





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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=%282%29%28x--2%29 Plug in m=2, x%5B1%5D=-2, and y%5B1%5D=0 (these values are given)



y-0=%282%29%28x%2B2%29 Rewrite x--2 as x%2B2



y-0=2x%2B%282%29%282%29 Distribute 2


y-0=2x%2B4 Multiply 2 and 2 to get 4%2F1. Now reduce 4%2F1 to get 4

y=2x%2B4%2B0 Add 0 to both sides to isolate y


y=2x%2B4 Combine like terms 4 and 0 to get 4

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Answer:



So the equation of the line which goes through the points (-2,0) and (0,4) is:y=2x%2B4


The equation is now in y=mx%2Bb form (which is slope-intercept form) where the slope is m=2 and the y-intercept is b=4


Notice if we graph the equation y=2x%2B4 and plot the points (-2,0) and (0,4), we get this: (note: if you need help with graphing, check out this solver)


Graph of y=2x%2B4 through the points (-2,0) and (0,4)


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




So we know the equation is y=2x%2B4