Question

change the following to slope intercept form
$8x - 4y = 14$
$6x + 3y = 21$
$2y - 3x = 20$
$1x - 3y = 0$
$- 4x - 6y = 12$
$2x - 5(3 + 2x) = 9$
solve the following equations:
$7x + 2 = 16$
$4z - 10.6 = - 7.4$
$7x - 24 = 25$
$\frac{c}{2.5} + 8.6 = 6.4$

Explanation:

Part 1: Convert to Slope-Intercept Form ($y=mx+b$)

Step1: Isolate $-4y$

$8x - 4y = 14 \implies -4y = -8x + 14$

Step2: Solve for $y$

$y = \frac{-8x}{-4} + \frac{14}{-4} \implies y = 2x - 3.5$

Step1: Isolate $3y$

$6x + 3y = 21 \implies 3y = -6x + 21$

Step2: Solve for $y$

$y = \frac{-6x}{3} + \frac{21}{3} \implies y = -2x + 7$

Step1: Isolate $2y$

$2y - 3x = 20 \implies 2y = 3x + 20$

Step2: Solve for $y$

$y = \frac{3x}{2} + \frac{20}{2} \implies y = 1.5x + 10$

Step1: Isolate $-3y$

$x - 3y = 0 \implies -3y = -x + 0$

Step2: Solve for $y$

$y = \frac{-x}{-3} + \frac{0}{-3} \implies y = \frac{1}{3}x$

Step1: Isolate $-6y$

$-4x - 6y = 12 \implies -6y = 4x + 12$

Step2: Solve for $y$

$y = \frac{4x}{-6} + \frac{12}{-6} \implies y = -\frac{2}{3}x - 2$

Step1: Expand parentheses

$2x - 5(3 + 2x) = 9 \implies 2x - 15 - 10x = 9$

Step2: Combine like terms

$-8x - 15 = 9$

Step3: Isolate $-8x$

$-8x = 9 + 15 \implies -8x = 24$

Step4: Solve for $x$

$x = \frac{24}{-8} \implies x = -3$

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Part 2: Solve Single-Variable Equations

Step1: Isolate $7x$

$7x + 2 = 16 \implies 7x = 16 - 2$

Step2: Solve for $x$

$7x = 14 \implies x = \frac{14}{7} = 2$

Step1: Isolate $4z$

$4z - 10.6 = -7.4 \implies 4z = -7.4 + 10.6$

Step2: Solve for $z$

$4z = 3.2 \implies z = \frac{3.2}{4} = 0.8$

Step1: Isolate $7x$

$7x - 24 = 25 \implies 7x = 25 + 24$

Step2: Solve for $x$

$7x = 49 \implies x = \frac{49}{7} = 7$

Step1: Isolate $\frac{c}{2.5}$

$\frac{c}{2.5} + 8.6 = 6.4 \implies \frac{c}{2.5} = 6.4 - 8.6$

Step2: Solve for $c$

$\frac{c}{2.5} = -2.2 \implies c = -2.2 \times 2.5 = -5.5$

Answer:

Slope-Intercept Form:

1. $y = 2x - 3.5$
2. $y = -2x + 7$
3. $y = 1.5x + 10$
4. $y = \frac{1}{3}x$
5. $y = -\frac{2}{3}x - 2$
6. $x = -3$

Solved Equations:

1. $x = 2$
2. $z = 0.8$
3. $x = 7$
4. $c = -5.5$