Question

write each equation in slope - intercept form.

1. $3x + 4y = 8$ 2) $9x + 35 = -5y$

1. $2y - 6 = -6x$ 4) $-11x - 7y = -56$

1. $\frac{5}{3}y = -(x - 5)$ 6) $-2(2x + y) = 28$

1. $-14x + y = 7$ 8) $12y = \frac{8x - 48}{3}$

1. $\frac{3(x - y)}{2} = 9$ 10) $\frac{2}{3}x + 4(y - 2) = 0$

Explanation:

1) Equation: $3x + 4y = 8$

Step1: Isolate the $y$-term

$4y = -3x + 8$

Step2: Solve for $y$

$y = -\frac{3}{4}x + 2$

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2) Equation: $9x + 35 = -5y$

Step1: Rearrange to isolate $y$-term

$-5y = 9x + 35$

Step2: Solve for $y$

$y = -\frac{9}{5}x - 7$

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3) Equation: $2y - 6 = -6x$

Step1: Isolate the $y$-term

$2y = -6x + 6$

Step2: Solve for $y$

$y = -3x + 3$

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4) Equation: $-11x - 7y = -56$

Step1: Isolate the $y$-term

$-7y = 11x - 56$

Step2: Solve for $y$

$y = -\frac{11}{7}x + 8$

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5) Equation: $\frac{5}{3}y = -(x - 5)$

Step1: Simplify the right-hand side

$\frac{5}{3}y = -x + 5$

Step2: Solve for $y$

$y = -\frac{3}{5}x + 3$

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6) Equation: $-2(2x + y) = 28$

Step1: Expand the left-hand side

$-4x - 2y = 28$

Step2: Isolate the $y$-term

$-2y = 4x + 28$

Step3: Solve for $y$

$y = -2x - 14$

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7) Equation: $-14x + y = 7$

Step1: Isolate $y$

$y = 14x + 7$

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8) Equation: $12y = \frac{8x - 48}{3}$

Step1: Simplify the right-hand side

$12y = \frac{8}{3}x - 16$

Step2: Solve for $y$

$y = \frac{2}{9}x - \frac{4}{3}$

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9) Equation: $\frac{3(x - y)}{2} = 9$

Step1: Eliminate the denominator

$3(x - y) = 18$

Step2: Expand and isolate $y$-term

$3x - 3y = 18 \implies -3y = -3x + 18$

Step3: Solve for $y$

$y = x - 6$

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10) Equation: $\frac{2}{3}x + 4(y - 2) = 0$

Step1: Expand the left-hand side

$\frac{2}{3}x + 4y - 8 = 0$

Step2: Isolate the $y$-term

$4y = -\frac{2}{3}x + 8$

Step3: Solve for $y$

$y = -\frac{1}{6}x + 2$

Answer:

1. $y = -\frac{3}{4}x + 2$
2. $y = -\frac{9}{5}x - 7$
3. $y = -3x + 3$
4. $y = -\frac{11}{7}x + 8$
5. $y = -\frac{3}{5}x + 3$
6. $y = -2x - 14$
7. $y = 14x + 7$
8. $y = \frac{2}{9}x - \frac{4}{3}$
9. $y = x - 6$
10. $y = -\frac{1}{6}x + 2$