SOLUTION: what is the slope-intercept form of the equation of a line that passes through (5,-4) and has a slope of '3/4'?

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Question 1167851: what is the slope-intercept form of the equation of a line that passes through
(5,-4) and has a slope of '3/4'?

Found 2 solutions by Theo, Edwin McCravy:
Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
the slope intercept form of the equation of a straight line is:

y = mx + b

m is the slope
b is the y-intercept.

if your know the slope, then just replace m with it and solve for b by replacing x and y in the equation with the value of one of the points.

in your problem, m = 3/4 and the point that it goes through is (x,y) = (5,-4)

replace m with 3/4 and replace x with 5 and y with -4 to get:

y = mx + b becomes -4 = 3/4 * 5 + b

simplify to get:

-4 = 3.75 + b

subtract 3.75 from both sides of the equation to get:

-4 - 3.75 = b

solve for b to get:

b = -7.75

the equation becomes:

y = 3/4 * x - 7.7 5

the graph of the equation looks like this.



you can see that the y-intercept (the value of y when x = 0) is -7.75 and that the graph of the equation goes through the point (x,y) = (5,-4).




Answer by Edwin McCravy(20056) About Me  (Show Source):
You can put this solution on YOUR website!
what is the slope-intercept form of the equation of a line that passes through
(5,-4) and has a slope of '3/4'?
There are two ways, One way uses the point-slope form 
and the other uses only the slope-intercept form.

First way [uses point-slope form]:

y-y%5B1%5D=m%28x-x%5B1%5D%29
y-%28-4%29=expr%283%2F4%29%28x-5%29
y%2B4=expr%283%2F4%29x-expr%283%2F4%29%2A5
y%2B4=expr%283%2F4%29x-15%2F4
y=expr%283%2F4%29x-15%2F4-4
y=expr%283%2F4%29x-15%2F4-16%2F4
y=expr%283%2F4%29x-31%2F4

Second way [uses only slope-intercept form]: 

y=mx%2Bb
-4=expr%283%2F4%29%285%29%2Bb
-4=15%2F4%2Bb
-16=15%2B4b
-31=4b
-31%2F4=b
y=expr%283%2F4%29x-31%2F4

Edwin