Question

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

Answer 1

Slope is `-1`, `y` intercept is `2`.

Explanation:

The equation of the graph is given in the form

`y=mx+b=-x+2`

where `m` is the gradient or slope, and `b` is the intercept on the `y` axis.

By simply comparing the two equations, we can see that `m=-1` and `b=2`.

This means the graph has a slope of `-1`, and crosses the `y` axis at point `(0,2)`.

Answer 2

Gradient (slope) = -1
y-intercept`->(x,y)=(0,2)`
x-intercept`->(x,y)=(2,0`

Explanation:

Compare to `y=mx+c`

`m-> "gradient (slope)"`
`c -> "y-intercept"`

Given:`" "y=-x+2`
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
`color(blue)("Determine gradient")`

Write as:`" "y=[(-1)xx x]+2`

`color(blue)("The gradient "->m=-1`
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
`color(blue)("Determine y-intercept")`

`color(blue)("y-intercept"->c=2`

`color(brown)("To prove y-intercept = 2")`

The graph crosses the y-axis at x=0. Substituting this value:

`color(brown)(y=-x+2" "->" "color(blue)(y=-(0)+2 = 2`

'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
`color(blue)("Determine x-intercept")`

The graph crosses the x-axis at y=0. Substituting this value

`" "0=-x+2`

Add `x` to both sides

`" "0+x=-x+x+2`

`color(blue)(" "x=0+2`
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~