Linear Equations
Linear equations are typically organized in slope-intercept form: [tex]y=mx+b[/tex]
- m = the slope
- b = the y-intercept (the value of y when x=0)
To find the slope of a line (m):
- Find the coordinates of two points that fall on the line
- Plug them into the following formula:
- [tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex] where [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex] are the coordinates of the points
To find the y-intercept of a line (b):
- Plug the slope into [tex]y=mx+b[/tex]
- Plug in one of the points
- Solve for b
Solving the Question
We're given a set of coordinates for this linear relation.
First, solve for the slope.
[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]
⇒ Plug in any two points that fall on the line (in this case we used (-2,-7) and (2,1)):
[tex]m=\dfrac{1-(-7)}{2-(-2)}\\\\m=\dfrac{1+7}{2+2}\\\\m=\dfrac{8}{4}\\\\m=2[/tex]
Therefore, the slope of the line is 2. Plug this into [tex]y=mx+b[/tex]:
[tex]y=2x+b[/tex]
Now, let's solve for the y-intercept (b)
[tex]y=2x+b[/tex]
Plug in any of the given points:
[tex]1=2(2)+b\\1=4+b\\b=-3[/tex]
Therefore, the y-intercept of the line is 3. Plug this back into [tex]y=2x+b[/tex]:
[tex]y=2x-3[/tex]
Answer
[tex]y=2x-3[/tex]
