Question

How do you find the slope and intercept of `5-x = y/3`?

Answer 1

The slope is 3 and the y-intercept is -15.

Explanation:

To solve this problem, we must first put the original equation in slope-intercept form. To do this, we'll multiply each side by 3 to get `15-3x=y`, or `y=3x-15`. From here, it's easy to find the slope and intercept. Since slope-intercept form is `y=mx+b`, where m is the slope and b is the y-intercept, the slope is 3 and the y-intercept is -15.

Answer 2

`color(blue)(x_("intercept")=5)`

`color(blue)(y_("intercept")=15)`

`color(blue)("The slope is "-3)`

Explanation:

Given:`" "5-x=y/3`

Multiply both sides by 3

`3(5-x)=yxx3/3`

But `3/3 =1`

`y=3(5-x)`

Multiply everything inside the brackets by 3

`y=15-3x`

The slope is the number (coefficient) in front of the `x`

`color(blue)("So the slope is "-3)`

'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
This means that as you read from left to right: for every 1 along you go down by 3. If the slope had been +3 that would mean you go up by 3 for every 1 along.
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
`color(blue)("To determine y-intercept")`

The `y_("intercept")` is the constant of 15 from `y=-3x+15`

`color(blue)(y_("intercept")=15)`
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
`color(blue)("To determine x-intercept")`

`color(brown)("Calculation shown in a lot of detail")`
`color(brown)("Normally a lot od steps would be skipped")`

The `x_("intercept")` is when y=0

`0=-3x+15`

Subtract 15 from both sides

`-15=-3x+0`

divide both sides by 3

`-15/3=x xx -3/3`

`-5=-x`

Multiply everything by (-1)

`5=x`

`x=5`

`color(blue)(x_("intercept")=5)`