Question

LOTS OF POINTS!?!?!?Write a linear function f with the values f(5)=−1 and f(0)=−1.
f(x)=

Answer 1

The euation of the linear function is:

• y = -1

Explanation:

As the function has the values

• at x = 5, f(5) = -1

• at x = 0, f(0) = -1

Thus, the two points are:

• (5, -1)

• (0, -1)

Finding the slope between (5, -1) and (0, -1)

`\mathrm{Slope}=(y_2-y_1)/(x_2-x_1)`

`\left(x_1,\:y_1\right)=\left(5,\:-1\right),\:\left(x_2,\:y_2\right)=\left(0,\:-1\right)`

`m=(-1-\left(-1\right))/(0-5)`

`m=0`

We know that the slope-intercept form of the line equation is

y=mx+b

where m is the slope and b is the y-intercept

We also know that the y-intercept can be computed by setting x=0 and finding the corresponding value of y.

so at x = 0, y = -1

Thus, the y-intercept 'b' = -1

Now, substituting m = 0 and b = -1 in the slope-intercept form of the line equation

y = mx+b

y = 0x + -1

y = -1

Therefore, the euation of the linear function is:

• y = -1