Question

Given the equation 3x – 4y = 24. 3 parts

a) Find two solutions to the equation. Show your work. Write your answer as coordinates.

b) Using your answers from part a, what is the slope of the given equation. Show your work.

c) Convert the given equation into slope-intercept form. Show your work.

Answer 1

a. (0,-6) and (8,0)

b.
`m = 3/4`

c.
`y = 3x/4 - 6`

Explanation:

Given

`3x - 4y = 24`

Solving (a): Two solutions

To determine the solutions of the equation, we assume values for x and y.

First: Let, x = 0

Substitute 0 for x in the equation

`3x - 4y = 24`

`3(0) - 4y = 24`

`- 4y = 24`

Divide both sides by -4

`y = 24/-4`

`y = -6`

So, one solution is (0,-6)

To determine another solution, we assume that y = 0

Substitute 0 for y in the equation

`3x - 4y = 24`

`3x -4(0) = 24`

`3x = 24`

Divide both sides by 3

`x = 24/3`

`x = 8`

So, another solution is (8,0)

Solving (b): The slope of the equation

We have to get the equation in the form:
`y = mx + b`

Where

`m = slope`

`3x - 4y = 24`

Subtract 3x from both sides

`3x - 3x - 4y = 24 - 3x`

`- 4y = 24 - 3x`

Divide both sides by -4

`y = 24/-4 - 3x/-4`

`y = -6 + 3x/4`

`y = 3x/4 - 6`

By comparison,

`m = 3/4`

Hence:

`Slope = 3/4`

Solving (c): Slope intercept form

This has been solved in (b) above

`y = 3x/4 - 6`