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.

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boffeemadrid boffeemadrid · Answer 1 · 2020-11-05T12:46:39+01:00

Answer:

[tex](1,-5.25)[/tex] and [tex](2,-4.5)[/tex]

[tex]y=\dfrac{3}{4}x-6[/tex]

Step-by-step explanation:

The equation of the line is [tex]3x-4y=24[/tex]

Let us take [tex]x=1[/tex]

[tex]3\times1-4y=24\\\Rightarrow y=\dfrac{24-3}{-4}\\\Rightarrow y=-5.25[/tex]

Let us take [tex]x=2[/tex]

[tex]3\times2-4y=24\\\Rightarrow y=\dfrac{24-6}{-4}\\\Rightarrow y=-4.5[/tex]

Two solutions of the equation are [tex](1,-5.25)[/tex] and [tex](2,-4.5)[/tex]

Slope is given by

[tex]m=\dfrac{y_2-y_1}{x_2-x_1}\\\Rightarrow m=\dfrac{-4.5-(-5.25)}{2-1}\\\Rightarrow m=\dfrac{3}{4}[/tex]

The slope of the equation is [tex]\dfrac{3}{4}[/tex]

[tex]3x-4y=24\\\Rightarrow y=\dfrac{3x-24}{4}\\\Rightarrow y=\dfrac{3}{4}x-6[/tex]

The slope intercept form of the equation is [tex]y=\dfrac{3}{4}x-6[/tex]