SOLUTION: Write the slope-intercept equation of the line that contains the points (-4,-2) and (11,-14). Include the formulas used to complete the work.

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons  -> Quadratic Equation Lesson -> SOLUTION: Write the slope-intercept equation of the line that contains the points (-4,-2) and (11,-14). Include the formulas used to complete the work.      Log On


   

Question 1205639: Write the slope-intercept equation of the line that contains the points (-4,-2) and (11,-14). Include the formulas used to complete the work.
Found 2 solutions by josgarithmetic, math_tutor2020:
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
Write the slope-intercept equation of the line that contains the points (-4,-2) and (11,-14).
Include the formulas used to complete the work.
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Write the slope-intercept equation of the line that contains the points (p,v) and (h,k).
Include the formulas used to complete the work.
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Slope-Intercept Equation Form, y=mx+b.

y-k=%28%28v-k%29%2F%28p-h%29%29%28x-h%29-----starting in point-slope form;

y-k=%28%28v-k%29%2F%28p-h%29%29x-%28%28v-k%29%2F%28p-h%29%29h
highlight_green%28y=%28%28v-k%29%2F%28p-h%29%29x%2Bk-%28%28v-k%29%2F%28p-h%29%29h%29
THIS IS in slope-intercept form.
m corresponds to %28v-k%29%2F%28p-h%29, and b corresponds to k-%28%28v-k%29%2F%28p-h%29%29h.

You can decide if this way below is easier or not:
y-%28-2%29=%28%28-2%2B14%29%2F%28-4-11%29%29%28x-%28-4%29%29
y%2B2=%2812%2F-15%29%28x%2B4%29
y%2B2=-%284%2F5%29%28x%2B4%29
y=-%284%2F5%29x-16%2F5-2
y=-%284%2F5%29x-16%2F5-10%2F5
highlight%28y=-%284%2F5%29x-26%2F5%29

Answer by math_tutor2020(3816) About Me  (Show Source):
You can put this solution on YOUR website!

Let's find the slope.




m+=+%28y%5B2%5D+-+y%5B1%5D%29%2F%28x%5B2%5D+-+x%5B1%5D%29

m+=+%28-14+-+%28-2%29%29%2F%2811+-+%28-4%29%29

m+=+%28-14+%2B+2%29%2F%2811+%2B+4%29

m+=+%28-12%29%2F%2815%29

m+=+-4%2F5
The slope is m = -4/5.
It will mean "go down 4, then right 5".

Now apply point-slope form.
y+-+y%5B1%5D+=+m%28x+-+x%5B1%5D%29

y+-+%28-2%29+=+-expr%284%2F5%29%28x+-+%28-4%29%29

y+%2B2+=+-expr%284%2F5%29%28x+%2B4%29

y+%2B2+=+-expr%284%2F5%29x+%2B+%28-4%2F5%29%2A%284%29

y+%2B2+=+-expr%284%2F5%29x+-16%2F5

y+=+-expr%284%2F5%29x+-16%2F5-2

y+=+-expr%284%2F5%29x+-16%2F5-10%2F5

y+=+-expr%284%2F5%29x+%2B%28-16-10%29%2F5

y+=+-expr%284%2F5%29x+-26%2F5

y+=+-0.8x+-+5.2
The result is in slope-intercept form (y = mx+b)
m = -4/5 = -0.8 = slope
b = -26/5 = -5.2 = y intercept

To verify, plug in x = -4 and you should get y = -2.
Also, plug in x = 11 and you should get y = -14.
I'll leave this verification scratch work for the student to do.
Desmos and GeoGebra are recommended graphing tools to visually verify the answer.