The slope of the line representing the linear function f(x) is determined as $-\frac{1}{2}$ . The function f(x) is decreasing because the slope is less than zero, i.e., m<0.

Step-by-step explanation:

A linear function f(x) is given with two points, (2,3) and (0,4) lying on the line representing f(x).

It is asked to determine the slope of the line and state if the function is increasing or decreasing. of the value of the slope obtained.

Step 1 of 1

Determine the slope of the line.

The points as given in the question are (2,3) and (0,4). Now, the formula for the slope is given as

$m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}$

So, substitute $4 \& 3$ for $y_{2}$ and $y_{1}$ respectively, and $0 \& 2$ for $x_{2}$ and $x_{1}$ respectively in the above formula. Then simplify to get the slope as follows, $m=\frac{4-3}{0-2}$\\ $m=\frac{1}{-2}$\\ $m=-\frac{1}{2}$

The slope of the line is obtained as $-\frac{1}{2}$ . Now, as $-\frac{1}{2} < 0$ , so the function f(x) is decreasing.

7 0

2 years ago

Find the area of a square with a diagonal of 8cm.

klio [65]

You have to use the Pythagorean theorem but there is a little twist here since a square has has equal sides. So:
x^2+x^2=8
2x^2=8
2/2x^2=8/2
x^2=4
√x^2=√4
x=2
The side of the square is 2.
So now the area of a square is:
Side×Side
2×2=4
The area of the square is 4 centimetres

7 0

3 years ago