Respuesta :
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 [tex]$y=\frac{1}{3} x-\frac{13}{3}$[/tex].
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,
[tex]$m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}$[/tex]
Substitute 2&4 for [tex]$y_{2}$[/tex] and [tex]$y_{1}$[/tex] respectively, and [tex]$5 \&-1$[/tex] for [tex]$x_{2}$[/tex] and [tex]$x_{1}$[/tex] respectively in the above formula. Then simplify to get the slope as follows,
[tex]m=\frac{2-4}{5-(-1)}$\\ $m=\frac{-2}{6}$\\ $m=-\frac{1}{3}$[/tex]
Step 2 of 3
Write the linear equation in point-slope form.
A linear equation in point slope form is given as,
[tex]$y-y_{1}=m\left(x-x_{1}\right)$[/tex]
Substitute [tex]$-\frac{1}{3}$[/tex] for m,-1 for [tex]$x_{1}$[/tex], and 4 for [tex]$y_{1}$[/tex] in the above equation and simplify using the distributive property as follows,
[tex]y-4=-\frac{1}{3}(x-(-1))$\\ $y-4=-\frac{1}{3}(x+1)$\\ $y-4=-\frac{1}{3} x-\frac{1}{3}$[/tex]
Step 3 of 3
Simplify the equation further.
Add 4 on each side of the equation [tex]$y-4=\frac{1}{3} x-\frac{1}{3}$[/tex], and simplify as follows,
[tex]y-4+4=\frac{1}{3} x-\frac{1}{3}+4$\\ $y=\frac{1}{3} x-\frac{1+12}{3}$\\ $y=\frac{1}{3} x-\frac{13}{3}$[/tex]
This is the required linear equation.
