Respuesta :
Answer:
The required linear equation satisfying the given conditions f(-1)=4 and f(5)=1 is [tex]$y=\frac{-1}{2} x+\frac{7}{2}$[/tex]
Step-by-step explanation:
It is given that f(-1)=4 and f(5)=1.
It is required to find out a linear equation satisfying the conditions f(-1)=4
and f(5)=1. linear equation of the line in the form
[tex]$\left(y-y_{2}\right)=m\left(x-x_{2}\right)$[/tex]
Step 1 of 4
Observe, f(-1)=4 gives the point (-1,4)
And f(5)=1 gives the point (5,1).
This means that the function f(x) satisfies the points (-1,4) and (5,1).
Step 2 of 4
Now find out the slope of a line passing through the points (-1,4) and (5,1),
[tex]$\begin{aligned}&m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}} \\&m=\frac{1-4}{5-(-1)} \\&m=\frac{-3}{5+1} \\&m=\frac{-3}{6} \\&m=\frac{-1}{2}\end{aligned}$[/tex]
Step 3 of 4
Now use the slope [tex]$m=\frac{-1}{2}$[/tex] and use one of the two given points and write the equation in point-slope form:
[tex]$(y-1)=\frac{-1}{2}(x-5)$[/tex]
Distribute [tex]$\frac{-1}{2}$[/tex],
[tex]$y-1=\frac{-1}{2} x+\frac{5}{2}$[/tex]
Step 4 of 4
This linear function can be written in the slope-intercept form by adding 1 on both sides,
[tex]$\begin{aligned}&y-1+1=\frac{-1}{2} x+\frac{5}{2}+1 \\&y=\frac{-1}{2} x+\frac{5}{2}+\frac{2}{2} \\&y=\frac{-1}{2} x+\frac{7}{2}\end{aligned}$[/tex]
So, this is the required linear equation.
