SOLUTION: Could someone please help with this problem: Give the equation of the line which passes through (-8, 11) and has a slope of -7/4. (that is m = -7/4) Give the equation in slope-i

Algebra ->  Linear-equations -> SOLUTION: Could someone please help with this problem: Give the equation of the line which passes through (-8, 11) and has a slope of -7/4. (that is m = -7/4) Give the equation in slope-i      Log On


   

Question 88160: Could someone please help with this problem:
Give the equation of the line which passes through (-8, 11) and has a slope of -7/4. (that is m = -7/4) Give the equation in slope-intercept form and standard form.
Thanks.
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 -7%2F4 which goes through the point (-8,11), 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-11=%28-7%2F4%29%28x--8%29 Plug in m=-7%2F4, x%5B1%5D=-8, and y%5B1%5D=11 (these values are given)

y-11=%28-7%2F4%29x-%28-7%2F4%29%28-8%29%29 Distribute -7%2F4

y-11=%28-7%2F4%29x%2B%287%2F4%29%28-8%29%29 Multiply the negatives

y-11=%28-7%2F4%29x%2B-56%2F4 Multiply 7%2F4 and -8 to get -56%2F4

y-11=%28-7%2F4%29x%2B-14 Reduce

y=%28-7%2F4%29x%2B-14%2B11Add 11 to both sides

y=%28-7%2F4%29x%2B-3 Combine like terms
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Answer:


So the equation of the line with a slope of -7%2F4 which goes through the point (-8,11) is:

y=%28-7%2F4%29x%2B-3 which is now in y=mx%2Bb form where the slope is m=-7%2F4 and the y-intercept is b=-3

Notice if we graph the equation y=%28-7%2F4%29x%2B-3 (note: if you need help with graphing, check out this solver) and plot the point (-8,11), we get

Graph of y=%28-7%2F4%29x%2B-3 through the point (-8,11)
and we can see that the point lies on the line. Since we know the equation has a slope of -7%2F4 and goes through the point (-8,11), this verifies our answer.




Now lets convert it to standard form

Solved by pluggable solver: Converting Linear Equations in Standard form to Slope-Intercept Form (and vice versa)
Convert from slope-intercept form (y = mx+b) to standard form (Ax+By = C)


y+=+%28-7%2F4%29x-3 Start with the given equation


4%2Ay+=+4%2A%28%28-7%2F4%29x-3%29 Multiply both sides by the LCD 4


4y+=+-7x-12 Distribute and multiply


4y%2B7x+=+-7x-12%2B7x Add 7x to both sides


7x%2B4y+=+-12 Simplify


The original equation y+=+%28-7%2F4%29x-3 (slope-intercept form) is equivalent to 7x%2B4y+=+-12 (standard form where A > 0)


The equation 7x%2B4y+=+-12 is in the form Ax%2BBy+=+C where A+=+7, B+=+4 and C+=+-12






Answer:
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So the equation in slope-intercept is

y=%28-7%2F4%29x%2B-3

and the equation in standard form is

7x%2B4y=-12