SOLUTION: Write the equation of the line with x-intercept (–3, 0) and y-intercept (0, –2).

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Question 85242: Write the equation of the line with x-intercept (–3, 0) and y-intercept (0, –2).
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Since we know the intercepts, we know 2 points on the line. So we have the points (-3,0) and (0,-2)

Solved by pluggable solver: Finding the Equation of a Line
First lets find the slope through the points (-3,0) 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 (-3,0) and (x%5B2%5D,y%5B2%5D) is the second point (0,-2))


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


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



So the slope is

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



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



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


y-0=%28-2%2F3%29x-2 Multiply -2%2F3 and 3 to get -6%2F3. Now reduce -6%2F3 to get -2

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


y=%28-2%2F3%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 (-3,0) and (0,-2) is:y=%28-2%2F3%29x-2


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


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


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


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