Question

1. Given the equation 3x – 4y = 24.

a) Find two solutions to the equation. Show your work. See pages 82 – 85 in your reference guide. Write your answer as coordinates.





b) Using your answers from part a, what is the slope of the given equation. Show your work. See pages 88 – 90 in your reference guide.






c) Convert the given equation into slope-intercept form. Show your work. See page 91 - 93 in your reference guide.

Answer 1

`(1,-5.25)` and
`(2,-4.5)`

`y=(3)/(4)x-6`

`y=(3)/(4)x-6`

Explanation:

The equation of the line is
`3x-4y=24`

Let us take
`x=1`

`3*1-4y=24\\\Rightarrow y=(24-3)/(-4)\\\Rightarrow y=-5.25`

Let us take
`x=2`

`3*2-4y=24\\\Rightarrow y=(24-6)/(-4)\\\Rightarrow y=-4.5`

Two solutions of the equation are
`(1,-5.25)` and
`(2,-4.5)`

Slope is given by

`m=(y_2-y_1)/(x_2-x_1)\\\Rightarrow m=(-4.5-(-5.25))/(2-1)\\\Rightarrow m=(3)/(4)`

The slope of the equation is
`(3)/(4)`

`3x-4y=24\\\Rightarrow y=(3x-24)/(4)\\\Rightarrow y=(3)/(4)x-6`

The slope intercept form of the equation is
`y=(3)/(4)x-6`