Question

What is the slope of a line defined by the equation 3x + y = -4?

Answer 1

slope`=-3`

Explanation:

Recall that the slope of a line can be determined when its equation is in slope-intercept form:

`color(blue)(|bar(ul(color(white)(a/a)y=mx+bcolor(white)(a/a)|)))`

where:
`y=`y-coordinate
`m=`slope
`x=`x-coordinate
`b=`y-intercept

In your case, you are looking for `m`.

Given,

`3x+y=-4`

Solve for `y`. Subtract `3x` from both sides.

`3xcolor(white)(i)color(red)(-3x)+y=color(red)(-3x)-4`

Simplifying,

`y=color(darkorange)(-3)x-4`

Referring back to the general equation of a line, the slope, `m`, would be `color(darkorange)(-3)`.