SOLUTION: slope 5;y intercept ;(0.4) slope 3/4;y intercept (0,8)

Algebra ->  Linear-equations -> SOLUTION: slope 5;y intercept ;(0.4) slope 3/4;y intercept (0,8)      Log On


   

Question 90122This question is from textbook beginning algebra
: slope 5;y intercept ;(0.4)
slope 3/4;y intercept (0,8) This question is from textbook beginning algebra

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 (0,4), 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-4=%285%29%28x-0%29 Plug in m=5, x%5B1%5D=0, and y%5B1%5D=4 (these values are given)

y-4=%285%29x-%285%29%280%29%29 Distribute 5

y-4=%285%29x%2B%28-5%29%280%29%29 Multiply the negatives

y-4=%285%29x%2B0 Multiply -5 and 0 to get 0

y=%285%29x%2B0%2B4Add 4 to both sides

y=5x%2B4 Combine like terms
------------------------------------------------------------------------------------------------------------
Answer:


So the equation of the line with a slope of 5 which goes through the point (0,4) is:

y=5x%2B4 which is now in y=mx%2Bb form where the slope is m=5 and the y-intercept is b=4

Notice if we graph the equation y=5x%2B4 and plot the point (0,4), we get (note: if you need help with graphing, check out this solver)

Graph of y=5x%2B4 through the point (0,4)
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 (0,4), this verifies our answer.

-----------------------------------------------------------------



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
------------------------------------------------------------------------------------------------------------
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.