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Find an equation of the line that goes through the points (8,-45) and (2,-9). Write your answer in the form y = mx + b.

User Moki
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1 Answer

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Linear Equations

Linear equations are commonly organized in slope-intercept form:


y=mx+b

  • m = slope
  • b = the y-intercept (the value of y when x=0)

To find the equation of a line given two points:

  1. Determine the slope of the line using the slope formula
  2. Plug the slope into
    y=mx+b
  3. Determine the y-intercept by solving for b
  4. Plug the y-intercept back into the equation

Solving the Question

We're given:

  • The line passes through the points (8,-45) and (2,-9)

First, determine the slope using the following formula:


m=(y_2-y_1)/(x_2-x_1) where the given points are
(x_1,y_1) and
(x_2,y_2)

⇒ Plug in the given points (8,-45) and (2,-9):


m=(-45-(-9))/(8-2)\\\\m=(-45+9)/(8-2)\\\\m=(-36)/(6)\\\\m=-6

Therefore, the slope of the line is -6. Plug this into
y=mx+b as m:


y=-6x+b

Now, determine the y-intercept:


y=-6x+b

⇒ Plug in one of the given points as (x,y) and solve for b:


-9=-6(2)+b\\-9=-12+b\\3=b

Therefore the y-intercept of the line is 3. Plug this back into
y=-6x+b:


y=-6x+3

Answer


y=-6x+3

User Joshua Kravitz
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