Question

Find the equation of the line that satisfies f( - 1) = 4 and f(5) = 1. Use x for input and y for output,

and write your answer in slope intercept form.

Answer 1

Answer: y=-1/2x+7/2

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
`(y_(2)-y_(1) )/(x_(2)-x_(1) )`.

`(1-4)/(5-(-1)) =(-3)/(6)=-(1)/(2)`

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]

`b=(7)/(2)`

Now that we have the y-intercept, we can complete the equation.

y=-1/2x+7/2