Question

Find the linear function with the following properties.

f(−4)=6
Slope of f=−6

Answer 1

Given:

f(−4)=6

Slope of f=−6

To find:

The linear function with the given properties.

Solution:

We have,

f(−4)=6

It means, the value of linear function is 6 at x=-4. So, the linear function passes through the point (-4,6).

Slope of f=−6

The point slope form of a linear function is

$y-y_1=m(x-x_1)$

where, m is slope of the linear function.

On substituting the values, we get

$y-6=(-6)(x-(-4))$

$y-6=-6(x+4)$

$y-6=-6x-24$

Add 6 on both sides.

$y-6+6=-6x-24+6$

$y=-6x-18$

The function form of this linear equation is

$f(x)=-6x-18$

Therefore, the required function is $f(x)=-6x-18$.