Linear Equations
Linear equations are commonly organized in slope-intercept form:
[tex]y=mx+b[/tex]
- m = slope
- b = the y-intercept (the value of y when x=0)
To find the equation of a line given two points:
- Determine the slope of the line using the slope formula
- Plug the slope into [tex]y=mx+b[/tex]
- Determine the y-intercept by solving for b
- 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:
[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex] where the given points are [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex]
⇒ Plug in the given points (8,-45) and (2,-9):
[tex]m=\dfrac{-45-(-9)}{8-2}\\\\m=\dfrac{-45+9}{8-2}\\\\m=\dfrac{-36}{6}\\\\m=-6[/tex]
Therefore, the slope of the line is -6. Plug this into [tex]y=mx+b[/tex] as m:
[tex]y=-6x+b[/tex]
Now, determine the y-intercept:
[tex]y=-6x+b[/tex]
⇒ Plug in one of the given points as (x,y) and solve for b:
[tex]-9=-6(2)+b\\-9=-12+b\\3=b[/tex]
Therefore the y-intercept of the line is 3. Plug this back into [tex]y=-6x+b[/tex]:
[tex]y=-6x+3[/tex]
Answer
[tex]y=-6x+3[/tex]
