Question

What is the slope of `2y=-2y+6x+9`?

Answer 1

The slope is `3/2` or `1.5`.

Explanation:

`2y = -2y + 6x + 9`

To find the slope, first make the equation in slope-intercept form, shown here:

When we put it in this form we can find the slope easily as it is the number multiplied by `x`.

`2y = -2y + 6x + 9`

First, add `color(blue)(2y)` to both sides of the equation:
`2y quadcolor(blue)(+quad2y) = -2y + 6x + 9 quadcolor(blue)(+quad2y)`

`4y = 6x + 9`

Now divide both sides by `color(blue)4`:
`(4y)/color(blue)4 = (6x+9)/color(blue)4`

`y = 6/4x + 9/4`

Simplify:
`y = 3/2x + 9/4`

Since we said earlier that the slope is the number multiplied by `x`, we know that the slope is `3/2` or `1.5`.

Hope this helps!