Question

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.

Answer 1

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`