Question

What is the slope and intercept of `4x+y=1`?

Answer 1

Slope: `(-4)`
y-intercept`=1color(white)("XXXX")`x-intercept`=1/4`

Explanation:

For a linear equation in the general form:
`color(white)("XXX")color(red)(A)x+color(blue)(B)y=C`
the slope is `m=-color(red)(A)/color(blue)(B)`

For the given equation `color(red)(4)x+y=1rArrcolor(red)(4)x+color(blue)(1)y=1`
this becomes `m=-color(red)(4)/color(blue)(1)`

Alternately, you could convert the equation into slope-intercept form:
`color(white)("XXX")4x+y=1 rArr y=color(green)(-4)x+color(brown)(1)`
with slope `color(green)(-4)` and y-intercept `color(brown)(1)`
The advantage of this method is that it gives you the value of the y-intercept directly (`color(brown)(1)` in this case).

Otherwise the value of the y-intercept is the value of `y` when `x=0`
`color(white)("XXX")4x+y=1` with `x=0`
`color(white)("XXX")rarr 4(0)+y=1`
`color(white)("XXX")rarr y=1`

The x-intercept can be found in a similar manner.
The value of the x-intercept is the value of `x` when `y=0`
`color(white)("XXX")4x+y=1` with `y=0`
`color(white)("XXX")rarr 4x+0=1`
`color(white)("XXX")rarr x=1/4`