Question

I’m unsure of what this is. help someone

Answer 1

Part 1)

Let's analyze each part of the function:

FROM x = 0 TO x = 5:

We can find the equation of this line by using The Slope-Intercept Form of the Equation of a Line, that states:

`The \ graph \ of \ the \ equation: \\ \\ y=mx+b \\ \\ is \ a \ line \ whose \ slope \ is \ m \ and \ whose \ y-intercept \ is \ (0, b)`

So the y-intercept here is
`(0,4)` and
`m=(4)/(5)`, therefore:

`\boxed{y=(4)/(5)x+4}`

FROM x = 0 TO x = 5:

From the previous line, we know that at
`x=5` the output is:

`y=(4)/(5)x+4 \\ \\ y=(4)/(5)(5)+4 \\ \\ y=4+4=8`

So the point
`P_(1)(5,8)` lies on both lines.

For this new line, the slope is
`m=-(3)/(5)`

So, with the Point-Slope Form of the Equation of a Line we can find the equation of this other line:

`The \ equation \ of \ the \ line \ with \ slope \ m \\ passing \ through \ the \ point \ (x_(1),y_(1)) \ is:\\ \\ y-y_(1)=m(x-x_(1))`

So:

`y-8=-(3)/(5)(x-5) \\ \\ y=8-(3)/(5)x+3 \\ \\ \boxed{y=-(3)/(5)x+11}`

The graph is shown below.

Part 2)

The graph of the linear function
`f(x)=ax+b` is a line with slope
`m=a` and
`y-intercept` at
`(0,b)`. From the items, we can assure that the following equations are linear functions:

`\bullet 3y=2x-1.5 \ because \ y=(2)/(3)x-(1)/(2) \\ \\ \\ \bullet y=1 \ because \ y=m(0)+1 \\ \\ \\ \bullet 5(x+y)=-25 \ because \ 5x+5y=-25 \ \therefore 5y=-5x-25 \therefore y=-x-5`

In conclusion, the other functions are nonlinear and they are:

`\bullet \ y=x^2+3 \\ \\ \bullet \ y=x^3 \\ \\ \bullet \ y=12-x^2`