SOLUTION: Find the equation of the line passing through the given points. write the equation in function notation. (2,-8) and (-4,-3)

Algebra ->  Equations -> SOLUTION: Find the equation of the line passing through the given points. write the equation in function notation. (2,-8) and (-4,-3)      Log On


   

Question 671693: Find the equation of the line passing through the given points. write the equation in function notation. (2,-8) and (-4,-3)
Found 2 solutions by lwsshak3, ReadingBoosters:
Answer by lwsshak3(11628) About Me  (Show Source):
You can put this solution on YOUR website!
Find the equation of the line passing through the given points. write the equation in function notation. (2,-8) and (-4,-3)
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Equation of a line: f(x)=mx+b, m=slope, b=y-intercept
slope=∆y/∆x
=(-8-(-3))/(2-(-4))
=(-8+3)/(2+4)
m=-5/6
Equation:
f(x)=-5x/6+b
solve for b using coordinates of one of given points (2,-8)
-8=-5*2/6+b
-48=-10+6b
6b=-38
b=-38/6=-19/3
Equation:
f(x)=-5x/6-19/3

Answer by ReadingBoosters(3246) About Me  (Show Source):
You can put this solution on YOUR website!
Start with finding the slope
...
slope = %28y1-y2%29%2F%28x1-x2%29+=+%28-8--3%29%2F%282--4%29+=+-5%2F6
...
Use either coordinate and the slope to solve for b, y-intercept
-8 = -5%2F6(2) + b
-8 = -10%2F6 + b
b = -8 + 10%2F6 = -8%286%2F6%29+%2B+10%2F6+=+-48%2F6+%2B+10%2F6+=+-38%2F6+=+-19%2F3
...
Confirm using the other coordinate
y = -5%2F6(-4) + -19%2F3
y = 10%2F3+-+19%2F3+=+-9%2F3+=+-3
That's correct! (-4, -3)
...
So the equation for the line is...
y = -5%2F6x - 19%2F3
written as a function
highlight_green%28f%28x%29+=+%28-5%2F6%29x+-+%2819%2F3%29%29
.....................
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