Question

What is the slope and intercept for `x - y + 1 = 0` and how would you graph it?

Answer 1

Slope: `1`
y-intercept: `1`
x-intercept: `(-1)`

Explanation:

The general slope-intercept form for a line is
`color(white)("XXX")y=mx+b`
`color(white)("XXXXX")`where `m` is the slope and `b` is the y-intercept

`x-y+1=0`
can be converted into slope-intercept form by
adding `y` to both sides and then exchanging the sides:
`color(white)("XXX")x+1=y`
`color(white)("XXX")y=(1)x+1`
`color(white)("XXXXX")`Note that I have inserted the implied coefficient of `1` for `x`

Based on the general form we can see that
`color(white)("XXX")`the slope is `m=1`
and
`color(white)("XXX")`the y-intercept is `b=1`

Assuming the x-intercept is also required,
we note that the x-intercept is the value of `x` when `y=0`
`color(white)("XXX")x-(0)+1=0color(white)("XX")rarrcolor(white)("XX")x=-1`

The x and y-intercepts give us the points
`color(white)("XXX")(-1,0)` and `(0,1)` respectively.
If we plot these two points on the Cartesian plane and draw a straight line through them, we will obtain the required graph

graph{(x-y+1)((sqrt(x^2+(y-1)^2))-0.1)((sqrt((x+1)^2+y^2))-0.1)=0 [-5.25, 5.85, -2.02, 3.527]}