SOLUTION: write the slope intercept form of the following lines x-intercept: -3, y intercept:6

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Question 112935This question is from textbook Algebra 1
: write the slope intercept form of the following lines
x-intercept: -3, y intercept:6 This question is from textbook Algebra 1

Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Since the x-intercept is -3 and the y intercept is 6, the line goes through the points (-3,0) and (0,6)


First lets find the slope through the points (-3,0) and (0,6)

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 (0,6))

m=%286-0%29%2F%280--3%29 Plug in y%5B2%5D=6,y%5B1%5D=0,x%5B2%5D=0,x%5B1%5D=-3 (these are the coordinates of given points)

m=+6%2F3 Subtract the terms in the numerator 6-0 to get 6. Subtract the terms in the denominator 0--3 to get 3


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


y-0=%282%29%28x%2B3%29 Rewrite x--3 as x%2B3


y-0=2x%2B%282%29%283%29 Distribute 2

y-0=2x%2B6 Multiply 2 and 3 to get 6

y=2x%2B6%2B0 Add 0 to both sides to isolate y

y=2x%2B6 Combine like terms 6 and 0 to get 6
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Answer:


So the equation of the line which goes through the points (-3,0) and (0,6) is:y=2x%2B6

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=6

Notice if we graph the equation y=2x%2B6 and plot the points (-3,0) and (0,6), we get this: (note: if you need help with graphing, check out this solver)

Graph of y=2x%2B6 through the points (-3,0) and (0,6)

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