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

Explanation:

Given the equation 3x-4y = 24

The solution occurs at when x = 0 and y = 0

when x = 0:

3(0)-4y = 24

0-4y = 24

-4y = 24

y = 24/-4

y = -6

when y = 0

3x-4(0) = 24

3x = 24

x = 24/3

x = 8

Hence the solution (x, y) is expressed as (8, -6)

b) Slope of the given equation will be expressed as

m = y/x

From the coordinate, y = -6 x = 8

m = -6/8

m = -3/4

c) The equation of a line in slope-intercept form is expressed as y = mx+c

Rewrite the given equation in this form as shown

Given 3x – 4y = 24.

-4y = -3x+24

Divide through by -4

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

y = 3/4 x - 6

Hence the equation in slope intercept form is y = 3/4 x - 6