Question

Find the slope and the y-intercept of the line.

- 3x - 4y= -20
Write your answers in simplest form.

Answer 1

Slope:
`\displaystyle-(3)/(4)`

Y-intercept: 5

Explanation:

Linear equations are typically organized in slope-intercept form:
`y=mx+b`, where m is the slope and b is the y-intercept.

`-3x-4y=-20`

To find the slope and y-intercept of the given line, rearrange the equation into slope-intercept form. We can do this by isolating y.

Add 3x to both sides:

`-3x-4y+3x=-20+3x\\-4y=3x-20`

Divide both sides by -4:

`y=\displaystyle -(3)/(4) x+5`

Now, we can identify
`\displaystyle-(3)/(4)` to be in place of m, the slope, and 5 to be in place of b, the y-intercept. Here is a comparison:

`y=\displaystyle -(3)/(4) x+5`

`y=mx+b`

I hope this helps!

Answer 2

The slope is -3/4 and the y intercept is 5

Explanation:

- 3x - 4y= -20

Slope intercept form is

y = mx+b where m is the slope and b is the y intercept

Solve for y

Add 3x to each side

- 3x - 4y+3x=3x -20

-4y = 3x-20

Divide by -4

-4y/-4 = 3x/-4 -20/-4

y = -3/4 x+5

The slope is -3/4 and the y intercept is 5