SOLUTION: Could someone please help me with this I am having trouble with slopes. The question is write the equation on the line with given slopes and y intercepts.Then graph each line us

Algebra ->  Linear-equations -> SOLUTION: Could someone please help me with this I am having trouble with slopes. The question is write the equation on the line with given slopes and y intercepts.Then graph each line us      Log On


   

Question 90115: Could someone please help me with this I am having trouble with slopes.
The question is write the equation on the line with given slopes and y intercepts.Then graph each line using the slope and y intercepts.
1)SLOPE 5:Y INTERCEPT:(0.2)
2)SLOPE 3/4:Y INTERCEPT (0,8)
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

If you want to find the equation of line with a given a slope of 5 which goes through the point (0,2), you can simply use the point-slope formula to find the equation:


---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 the given point

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

y-2=%285%29%28x-0%29 Plug in m=5, x%5B1%5D=0, and y%5B1%5D=2 (these values are given)

y-2=%285%29x-%285%29%280%29%29 Distribute 5

y-2=%285%29x%2B%28-5%29%280%29%29 Multiply the negatives

y-2=%285%29x%2B0 Multiply -5 and 0 to get 0

y=%285%29x%2B0%2B2Add 2 to both sides

y=5x%2B2 Combine like terms
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Answer:


So the equation of the line with a slope of 5 which goes through the point (0,2) is:

y=5x%2B2 which is now in y=mx%2Bb form where the slope is m=5 and the y-intercept is b=2

Notice if we graph the equation y=5x%2B2 and plot the point (0,2), we get (note: if you need help with graphing, check out this solver)

Graph of y=5x%2B2 through the point (0,2)
and we can see that the point lies on the line. Since we know the equation has a slope of 5 and goes through the point (0,2), this verifies our answer.

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If you want to find the equation of line with a given a slope of 3%2F4 which goes through the point (0,8), you can simply use the point-slope formula to find the equation:


---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 the given point

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

y-8=%283%2F4%29%28x-0%29 Plug in m=3%2F4, x%5B1%5D=0, and y%5B1%5D=8 (these values are given)

y-8=%283%2F4%29x-%283%2F4%29%280%29%29 Distribute 3%2F4

y-8=%283%2F4%29x%2B%28-3%2F4%29%280%29%29 Multiply the negatives

y-8=%283%2F4%29x%2B0 Multiply -3%2F4 and 0 to get 0

y=%283%2F4%29x%2B0%2B8Add 8 to both sides

y=%283%2F4%29x%2B8 Combine like terms
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Answer:


So the equation of the line with a slope of 3%2F4 which goes through the point (0,8) is:

y=%283%2F4%29x%2B8 which is now in y=mx%2Bb form where the slope is m=3%2F4 and the y-intercept is b=8

Notice if we graph the equation y=%283%2F4%29x%2B8 and plot the point (0,8), we get (note: if you need help with graphing, check out this solver)

Graph of y=%283%2F4%29x%2B8 through the point (0,8)
and we can see that the point lies on the line. Since we know the equation has a slope of 3%2F4 and goes through the point (0,8), this verifies our answer.