Question

Identify the y-intercept of the following linear equation? `y = 20 + 3x color(white)("d")` y-intercept = (type in number only)

nothing

Answer 1

20

Explanation:

Y-intercept is when x is equal to 0:
Set x equal to 0 and solve:
`y= 20+3(0)`
`y=20`
`"y-int": (0,20)`

X-Intercept is when y is equal to 0:
`0= 20+3x`
`-20=3x`
`-20/3=x`
`"x-int": (-20/3,0)`

Answer 2

In the format required by the question we have:

`"y-intercept"=20`

Explanation:

`color(blue)("A bit of background:")`

The x-axis passes through the origin `->(x,y)=(0,0)`
The y-axis passes through the origin `->(x,y)=(0,0)`

So any plot that crosses the x-axis (x-intercept) happens when `y=0`

Also any plot the crosses the y-axis (y-intercept) happens at `x=0`
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
`color(blue)("Answering the question")`

If you substitute `0` where ever there is an `color(red)(x)` you get:

`color(green)(y=20+3color(red)(x)color(white)("dd") ->color(white)("dd")y=20+3(color(red)(0))color(white)("dd") ->color(white)("dd") y=20+0)`

So the y-intercept is at `(x,y)=(0,20)`