Linear Equations
Linear equations are typically organized in slope-intercept form:
![y=mx+b](https://img.qammunity.org/2023/formulas/mathematics/high-school/smsb8cbft03lwblmi49nf2l6jby2ofxzws.png)
- 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:
where
and
are the coordinates of the points
To find the y-intercept of a line (b):
- Plug the slope into
![y=mx+b](https://img.qammunity.org/2023/formulas/mathematics/high-school/smsb8cbft03lwblmi49nf2l6jby2ofxzws.png)
- 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.
![m=(y_2-y_1)/(x_2-x_1)](https://img.qammunity.org/2023/formulas/mathematics/high-school/acimmv8dbausp5wbmaw14l0vkgzcnibr1g.png)
⇒ Plug in any two points that fall on the line (in this case we used (-2,-7) and (2,1)):
![m=(1-(-7))/(2-(-2))\\\\m=(1+7)/(2+2)\\\\m=(8)/(4)\\\\m=2](https://img.qammunity.org/2023/formulas/mathematics/high-school/c2g136ftd3vivpwwvemzamy7dbrvkwq80m.png)
Therefore, the slope of the line is 2. Plug this into
:
![y=2x+b](https://img.qammunity.org/2023/formulas/mathematics/college/nk11drug5mf634j25zir7448whk9rp74rq.png)
Now, let's solve for the y-intercept (b)
![y=2x+b](https://img.qammunity.org/2023/formulas/mathematics/college/nk11drug5mf634j25zir7448whk9rp74rq.png)
Plug in any of the given points:
![1=2(2)+b\\1=4+b\\b=-3](https://img.qammunity.org/2023/formulas/mathematics/high-school/ygcon531o82hoj17odsyjvj8v1b87ujiav.png)
Therefore, the y-intercept of the line is 3. Plug this back into
:
![y=2x-3](https://img.qammunity.org/2023/formulas/mathematics/high-school/3f76bvhffklm1pfpdq7o6cac6gxm96k96l.png)
Answer
![y=2x-3](https://img.qammunity.org/2023/formulas/mathematics/high-school/3f76bvhffklm1pfpdq7o6cac6gxm96k96l.png)