Question

How do you find the slope and intercept of `x= 2y+2`?

Answer 1

`color(blue)(y_("intercept")=-1)`
`color(blue)(x_("intercept")=2)`
`color(blue)("Gradient "=+2)`

Explanation:

`color(brown)("It does not matter if you have "x=2y+2" or by ")`
`color(brown)("manipulation "y=x/2-1 ". They both plot the same ")` `color(brown)("straight line.")`

So the slope `color(blue)("(gradient) is 2")`. That is: for every 1 along you go up 2. You always read from left to right for the gradient.

+2 means the line goes up whilst -2 means it goes down!
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

`color(blue)("To determine "x_("intercept"))`

The line will cross the x-axis at y=0

Set y=0 giving:

`x=2(0)+2`

`color(blue)(x_("intercept")=2)`

'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
`color(blue)("To determine "y_("intercept"))`

The line will cross the y-axis at x=0

Set x=0 giving:

`0=2y+2`

Subtract `color(red)( 2)` from both sides

`0color(red)(-2)=2y+2color(red)(-2)`

`-2=2y+0`

Divide both sides by `color(red)(2)`

`-2/(color(red)(2))=2/(color(red)(2)) xx y`

But `2/(-2)=-1" and "2/2=+1`

`-1=1xxy`

`color(blue)(y_("intercept")=-1)`
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~