Question

How do you find the slope of `y=7/5x-2`?

Answer 1

Slope: `7/5`

Explanation:

The slope-intercept form of a linear equation is
`color(white)("XXX")y=color(red)(m)x+color(blue)(b)`
`color(white)("XXXXXX")`where `color(red)(m)` is the slope and `color(blue)(b)` is the y-intercept.

`y= 7/5x-2 iff y=color(red)(7/5)x+color(blue)((-2))`

`color(white)("XXX")`is in this form

`rarr` slope `= color(red)(7/5)`

Alternative (if you don't know or are told not to use the slope-intercept form)

Slope `= m = (Delta y)/(Delta x)`

Pick two values for which `y=7/5x-2` is easy to calculate
(e.g. `x=0` and `x=5`) to get

Slope `= m = (y_(x=5) - y_(x=0))/(5-0)`

`color(white)("XXXXXXX")=(5-(-2))/5 = 7/5`