Question

What is slope and y intercept of 5x-10y=20?

Answer 1

The slope is `1/2`, and the y intercept is `-2`

Explanation:

First, you get y by itself. That gives you -10y=-5x+20. Then you divide both sides by -10. That gives you y=1/2x-2. The slope is the number with the variable and the y intercept is the other number.

---

Mathematical explanation

• `5x-10y=20`
• `-10y=-5x+20`
• `(-10y)/(-10)=(-5x)/(-10)+20/(-10)`
• `y=(5/10)x-2`
• `y=1/2x-2`

Now recall the format `y=\color(blue)(m)x+\color(red)(b)`, where `m` is the slope and `b` is the y-intercept.
From our equation, `y=\color(blue)(1/2)x+(\color(red)(-2))`, your slope is 1/2 and your y-intercept is -2.

Answer 2

`color(white)("dddd")`slope `=color(white)(-)1/2`

y-intercept `= -2`

Explanation:

Given: `5x-10y=20`

Before we do anything else notice that all the value are exactly divisible by 5 so lets simplify.

Divide everything by 5

`x-2y=4`

To make the `-2y` positive multiply all of both sides by (-1)

`-x+2y=-4`

Add `x` to both sides

`-x+2y=-4`
`ul(+x color(white)("dddd")=color(white)("dddd")+x )`
`0color(white)("d.")+2y=-4color(white)("d")+x`

Divide both sides by 2

`2/2y=-4/2+x/2`

`y=-2+1/2 x`

Change the order to match convention

`y=color(red)(1/2) xcolor(blue)(-2)`
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

The slope is the value in front of the `x` so the slope `color(red)(=1/2)`

The y-intercept (crosses the y-axis) is the constant of `color(blue)(-2)`