Answer: y=-1/2x+7/2
Step-by-step explanation:
For this problem, we are given f(-1)=4 and f(5)=1. This means the points are (-1,4) and (5,1). We can use the slope formula to find the slope. The formula is [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex].
[tex]\frac{1-4}{5-(-1)} =\frac{-3}{6}=-\frac{1}{2}[/tex]
Now that we know the slope, we can fill in what we know to solve for the y-intercept.
y=-1/2x+b
With any of the given points, we can plug in and solve for b.
4=-1/2(-1)+b [multiply]
4=1/2+b [subtract both sides by 1/2]
[tex]b=\frac{7}{2}[/tex]
Now that we have the y-intercept, we can complete the equation.
y=-1/2x+7/2
