Answer:
![y=\frac{4}{5}x-\frac{18}{5}](https://tex.z-dn.net/?f=y%3D%5Cfrac%7B4%7D%7B5%7Dx-%5Cfrac%7B18%7D%7B5%7D)
Step-by-step explanation:
Hi there!
We want to find the equation of the line that passes through the point (-3, -6) and (2, -2)
There are 3 ways to write the equation of the line:
- In slope-intercept form, which is y=mx+b, where m is the slope and b is the y intercept
- In point-slope form, which is
, where m is the slope and
is a point
- In standard form, which is ax+by=c, where a, b, and c are integer coefficients, but a and b cannot be zero, and a cannot be negative
The easiest way would either be slope-intercept or point-slope form, but let's write the equation in slope-intercept form, since it's the most common way
So we'll need to find the slope
The formula for the slope calculated from 2 points is
, where
and
are points
We have everything needed to find the slope, let's just label the values of the points to avoid any confusion:
![x_1=-3\\y_1=-6\\x_2=2\\y_2=-2](https://tex.z-dn.net/?f=x_1%3D-3%5C%5Cy_1%3D-6%5C%5Cx_2%3D2%5C%5Cy_2%3D-2)
Now substitute these values into the formula. Remember that m is the value of the slope:
m=![\frac{y_2-y_1}{x_2-x_1}](https://tex.z-dn.net/?f=%5Cfrac%7By_2-y_1%7D%7Bx_2-x_1%7D)
m=![\frac{-2--6}{2--3}](https://tex.z-dn.net/?f=%5Cfrac%7B-2--6%7D%7B2--3%7D)
Simplify the fraction:
m=![\frac{-2+6}{2+3}](https://tex.z-dn.net/?f=%5Cfrac%7B-2%2B6%7D%7B2%2B3%7D)
Add the numbers together:
m=![\frac{4}{5}](https://tex.z-dn.net/?f=%5Cfrac%7B4%7D%7B5%7D)
So the slope of the line is 4/5
Let's plug it into the formula y=mx+b, since we now know the value of m
y=
x+b
Now let's find b
As the equation passes through both (-3, -6) and (2, -2), we can use either point to help solve for b
Either point works, but let's take (2, -2) for instance
Substitute 2 as x and -2 as y
-2=4/5(2)+b
Multiply
-2=8/5+b
subtract 8/5 from both sides
-18/5=b
Now substitute -18/5 as b into the equation:
![y=\frac{4}{5}x-\frac{18}{5}](https://tex.z-dn.net/?f=y%3D%5Cfrac%7B4%7D%7B5%7Dx-%5Cfrac%7B18%7D%7B5%7D)
Hope this helps!