Mathematics

Question

14
What would be the slope of equation #1 in the following system? (Graphing)
2x+3y=12
4x-3y=15
(Worth 10 points )
A:1/2
B: -1
C:3/4
D:-2/3

1 Answer

  • Answer:

    [tex]m = -\frac{2}{3}[/tex]

    Step-by-step explanation:

    Given

    [tex]2x+3y=12[/tex]

    [tex]4x-3y=15[/tex]

    Required

    Slope of #1

    [tex]2x+3y=12[/tex]

    Make y the subject

    [tex]3y = -2x + 12[/tex]

    Divide through by 3

    [tex]y = -\frac{2}{3}x + \frac{12}{3}[/tex]

    [tex]y = -\frac{2}{3}x + 4[/tex]

    An equation has the form:

    [tex]y = mx + c[/tex]

    Where

    [tex]m = slope[/tex]

    Compare [tex]y = mx + c[/tex] and [tex]y = -\frac{2}{3}x + 4[/tex]

    [tex]m = -\frac{2}{3}[/tex]

    Hence, the slope is [tex]-\frac{2}{3}[/tex]

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