Question

What is the slope of `5y=1/3x+1`?

Answer 1

The slope is `1/15`
The intercept is `1/5`

Explanation:

To make progress it is necessary to write the equation of the line in the form

`y = mx + c`

where `m` is the slope and `c` is the intercept.

By inspection, you might note that division of `5y` by `5` will put the left hand side of the equation in a suitable form to compare it with the conventional slope-intercept form shown above. Remember that it will also be necessary to divide (every term in the) right hand side by `5`

That is,

`5y = 1/3 x + 1`

implies

`(5y)/5 = (1/3)/5 x + 1/5`

that is

`y = 1/15x + 1/5`

This is now in a suitable form to compare with `y = mx +c`

By inspection,

`m` corresponds to `1/15` so this is the slope
and
`c` corresponds to `1/5` so this is the intercept