Question

find the x and y intercepts
12x + 6y = 16
x - intercept

y - intercept

-6x - 3y = -9
x - intercept

y - intercept

-2x + 4y = -20
x - intercept

y - intercept

4x - 7y = 21
x - intercept

y - intercept

3x + 5y = 45
x - intercept

y - intercept

x - 2y = 10
x - intercept

y - intercept

Explanation:

For \(12x + 4y = 16\)

Step1: Find x-intercept, set \(y=0\)

\(12x + 4(0) = 16 \implies 12x = 16 \implies x = \frac{16}{12} = \frac{4}{3}\)

Step2: Find y-intercept, set \(x=0\)

\(12(0) + 4y = 16 \implies 4y = 16 \implies y = 4\)

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For \(-6x - 3y = -9\)

Step1: Find x-intercept, set \(y=0\)

\(-6x - 3(0) = -9 \implies -6x = -9 \implies x = \frac{-9}{-6} = \frac{3}{2}\)

Step2: Find y-intercept, set \(x=0\)

\(-6(0) - 3y = -9 \implies -3y = -9 \implies y = 3\)

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For \(-2x + 4y = -20\)

Step1: Find x-intercept, set \(y=0\)

\(-2x + 4(0) = -20 \implies -2x = -20 \implies x = 10\)

Step2: Find y-intercept, set \(x=0\)

\(-2(0) + 4y = -20 \implies 4y = -20 \implies y = -5\)

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For \(4x - 7y = 21\)

Step1: Find x-intercept, set \(y=0\)

\(4x - 7(0) = 21 \implies 4x = 21 \implies x = \frac{21}{4}\)

Step2: Find y-intercept, set \(x=0\)

\(4(0) - 7y = 21 \implies -7y = 21 \implies y = -3\)

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For \(3x + 5y = 45\)

Step1: Find x-intercept, set \(y=0\)

\(3x + 5(0) = 45 \implies 3x = 45 \implies x = 15\)

Step2: Find y-intercept, set \(x=0\)

\(3(0) + 5y = 45 \implies 5y = 45 \implies y = 9\)

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For \(x - 2y = 10\)

Step1: Find x-intercept, set \(y=0\)

\(x - 2(0) = 10 \implies x = 10\)

Step2: Find y-intercept, set \(x=0\)

\(0 - 2y = 10 \implies -2y = 10 \implies y = -5\)

Answer:

1. \(12x + 4y = 16\):

x-intercept: \(\frac{4}{3}\)
y-intercept: \(4\)

1. \(-6x - 3y = -9\):

x-intercept: \(\frac{3}{2}\)
y-intercept: \(3\)

1. \(-2x + 4y = -20\):

x-intercept: \(10\)
y-intercept: \(-5\)

1. \(4x - 7y = 21\):

x-intercept: \(\frac{21}{4}\)
y-intercept: \(-3\)

1. \(3x + 5y = 45\):

x-intercept: \(15\)
y-intercept: \(9\)

1. \(x - 2y = 10\):

x-intercept: \(10\)
y-intercept: \(-5\)