Question

How do you find the slope and intercept of `f(x) = 10x-7`?

Answer 1

Slope: `10`
`f(x)`-intercept: `(-7)`
`color(white)("XXX")x`-intercept: `7/10` (this may/may not) have been required)

Explanation:

The general slope-intercept form for a linear equation is
`color(white)("XXX")f(x)=color(green)(m)x+color(blue)(b)`
with slope `color(green)(m)` and `f(x)`-intercept `color(blue)(b)`

The given equation
`color(white)("XXX")f(x)=color(green)(10)xcolor(blue)(-7)`
is in this form with slope `color(green)(10)` and `f(x)`-intercept `color(blue)(""(-7))`

If the `x`-intercept is required:
the `x`-intercept is the value of `x` when `f(x)=0`
`color(white)("XXX")0=10x-7`
`color(white)("XXX")rarr 10x=7`
`color(white)("XXX")rarr x=7/10`

Answer 2

slope `=10` and the y-intercept = `-7`
The x-intercept is `7/10`

Explanation:

Remember that `f(x)` is the same as `y`.

`y = 10x-7`

This equation is therefore already in the form `y = mx + c`

The slope is 10 (the numerical coefficient of x) and the y-intercept is -7 (c)

To find the x-intercept, make y = 0 and solve for x

`10x = 7`
`x= 7/10`