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:

$m=\dfrac{y_2-y_1}{x_2-x_1}$ where the given points are $(x_1,y_1)$ and $(x_2,y_2)$

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

$m=\dfrac{-45-(-9)}{8-2}\\\\m=\dfrac{-45+9}{8-2}\\\\m=\dfrac{-36}{6}\\\\m=-6$

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

$y=-6x+3$