Question

How do you find the slope and intercept of `y-3/5x=-1/4`?

Answer 1

Slope: `3/5`
y-intercept: `-1/4`
x-intercept: `5/12`

Explanation:

A way to find the slope and intercepts of a linear equation is to transform it into the slope-intercept form. Generally the slope-intercept form looks like this:

`y = mx + b`

Where m is the slope and b is the y-intercept.

In this case, the given is `y - 3/5x = -1/4`, so we just have to transpose the term with the `x` variable into the other side of the equation.

[Solution]
`y - 3/5x = -1/4`
`y = 3/5x - 1/4`

Now that we have the slope-intercept form, we know from the equation that...

Slope -> `m = 3/5`
y-intercept: `-1/4`

As for the x-intercept, we know that when the graph crosses the x-axis then the value of `y` is 0. So in order to compute for the x-intercept, we only need to evaluate the equation with `y = 0`.

[Solution]
`y - 3/5x = -1/4`
`0 - 3/5x = -1/4`
`-3/5x = -1/4`
`3/5x = 1/4`
`x = (1/4)(5/3)`
`x = 5/12`