Question

How do you graph `5x+y=-5` using intercepts?

Answer 1

`x_("intercept")=-1`
`y_("intercept")=-5`

A lot of explanation given. Normally the calculation would be much faster than this.

Explanation:

Although the order is different this is an equation of a strait line.

Just for the hell of it letsw manipulate it into standardised form.

Subtract `color(red)(5x)` from both sides

`color(green)(5xcolor(red)(-5x)+y=color(red)(-5x)-5)`

But `5x-5x=0`

`0+y=-5x-5`

By changing `5x` on the left side to 0 it ends up on the other sides of = but with its sign changed to the opposite.
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Shortcut tips:

For add or subtract, move to the other side and reverse the sign action. Plus becomes minus and minus becomes plus.

For multiply or divide, move to the other side reverse the sign action. Divide becomes multiply and multiply becomes divide.
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`y=-5x-5`

The y-axis crosses the x-axis at `x=0` so to determine the y-intercept set `x=0`

`y_("intercept")=-5(0)-5`

`y_("intercept")=-5`

The x-axis crosses the y-axis at `y=0` so to determine the x-intercept set `y=0`

`y=0=-5x-5`

`0=-5x-5`

To make the `x` term positive multiply everything by (-1)
Note that `0xx(-1)=0`

`0=5x+5`

Subtract 5 from both sides

`-5=5x`

Divide both sides by 5

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

`-1=x`

`x_("intercept")=-1`