Question

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 of the equation of the equation will be gotten at the point where x = 0 and y = 0 as shown;

when x = 0

3(0)-4y = 24

0-4y = 24

y = 24/-4

y = -6

Also when y = 0

3x-4(0) = 24

3x = 24

x = 24/3

x = 8

Hence the solution of the equation (x, y) are (8, -6)

b) The standard from of equation of a line is y = mx+c where m is the slope. To get the slope of the line, we will need to rewire the equation in slope intercept form first.

Given 3x-4y = 24

-4y = 24-3x

-4y = -3x+24

Divide through by -4

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

y = 3/4 x - 6

Comparing

m = 3/4

Hence the slope of the line is 3/4

c) This has been done in (b) above. The equation in slope-intercept form is

y = 2/4 x - 6