Answer:
The linear equation for the line which passes through the points given as (-1,4) and (5,2), is written in the point-slope form as
.
Step-by-step explanation:
A condition is given that a line passes through the points whose coordinates are (-1,4) and (5,2).
It is asked to find the linear equation which satisfies the given condition.
Step 1 of 3
Determine the slope of the line.
The points through which the line passes are given as (-1,4) and (5,2). Next, the formula for the slope is given as,
![$m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}$](https://tex.z-dn.net/?f=%24m%3D%5Cfrac%7By_%7B2%7D-y_%7B1%7D%7D%7Bx_%7B2%7D-x_%7B1%7D%7D%24)
Substitute 2&4 for
and
respectively, and
for
and
respectively in the above formula. Then simplify to get the slope as follows,
![m=\frac{2-4}{5-(-1)}$\\ $m=\frac{-2}{6}$\\ $m=-\frac{1}{3}$](https://tex.z-dn.net/?f=m%3D%5Cfrac%7B2-4%7D%7B5-%28-1%29%7D%24%5C%5C%20%24m%3D%5Cfrac%7B-2%7D%7B6%7D%24%5C%5C%20%24m%3D-%5Cfrac%7B1%7D%7B3%7D%24)
Step 2 of 3
Write the linear equation in point-slope form.
A linear equation in point slope form is given as,
![$y-y_{1}=m\left(x-x_{1}\right)$](https://tex.z-dn.net/?f=%24y-y_%7B1%7D%3Dm%5Cleft%28x-x_%7B1%7D%5Cright%29%24)
Substitute
for m,-1 for
, and 4 for
in the above equation and simplify using the distributive property as follows,
![y-4=-\frac{1}{3}(x-(-1))$\\ $y-4=-\frac{1}{3}(x+1)$\\ $y-4=-\frac{1}{3} x-\frac{1}{3}$](https://tex.z-dn.net/?f=y-4%3D-%5Cfrac%7B1%7D%7B3%7D%28x-%28-1%29%29%24%5C%5C%20%24y-4%3D-%5Cfrac%7B1%7D%7B3%7D%28x%2B1%29%24%5C%5C%20%24y-4%3D-%5Cfrac%7B1%7D%7B3%7D%20x-%5Cfrac%7B1%7D%7B3%7D%24)
Step 3 of 3
Simplify the equation further.
Add 4 on each side of the equation
, and simplify as follows,
![y-4+4=\frac{1}{3} x-\frac{1}{3}+4$\\ $y=\frac{1}{3} x-\frac{1+12}{3}$\\ $y=\frac{1}{3} x-\frac{13}{3}$](https://tex.z-dn.net/?f=y-4%2B4%3D%5Cfrac%7B1%7D%7B3%7D%20x-%5Cfrac%7B1%7D%7B3%7D%2B4%24%5C%5C%20%24y%3D%5Cfrac%7B1%7D%7B3%7D%20x-%5Cfrac%7B1%2B12%7D%7B3%7D%24%5C%5C%20%24y%3D%5Cfrac%7B1%7D%7B3%7D%20x-%5Cfrac%7B13%7D%7B3%7D%24)
This is the required linear equation.