convert each equation below to slope - intercept form, then graph. show all work!
13. $8x - 2y = -14$
14. $x + y = 2$
15. $6x + 8y = -32$
16. $x - 2y = 0$
17. $8x - 4y = 16$
18. $3x - y = 3$

Question

Accepted Answer

### Problem 13: $ 8x - 2y = -14 $
# Explanation:
## Step 1: Isolate the $ y $-term
Subtract $ 8x $ from both sides:
$ -2y = -8x - 14 $

## Step 2: Solve for $ y $
Divide every term by $ -2 $:
$ y = \frac{-8x}{-2} + \frac{-14}{-2} $
$ y = 4x + 7 $

# Answer: Slope-intercept form: $ \boldsymbol{y = 4x + 7} $

### Problem 14: $ x + y = 2 $
# Explanation:
## Step 1: Isolate $ y $
Subtract $ x $ from both sides:
$ y = -x + 2 $

# Answer: Slope-intercept form: $ \boldsymbol{y = -x + 2} $

### Problem 15: $ 6x + 8y = -32 $
# Explanation:
## Step 1: Isolate the $ y $-term
Subtract $ 6x $ from both sides:
$ 8y = -6x - 32 $

## Step 2: Solve for $ y $
Divide every term by $ 8 $:
$ y = \frac{-6x}{8} + \frac{-32}{8} $
Simplify: $ y = -\frac{3}{4}x - 4 $

# Answer: Slope-intercept form: $ \boldsymbol{y = -\frac{3}{4}x - 4} $

### Problem 16: $ x - 2y = 0 $
# Explanation:
## Step 1: Isolate the $ y $-term
Subtract $ x $ from both sides:
$ -2y = -x $

## Step 2: Solve for $ y $
Divide every term by $ -2 $:
$ y = \frac{-x}{-2} $
$ y = \frac{1}{2}x $ (or $ y = 0.5x $)

# Answer: Slope-intercept form: $ \boldsymbol{y = \frac{1}{2}x} $

### Problem 17: $ 8x - 4y = 16 $
# Explanation:
## Step 1: Isolate the $ y $-term
Subtract $ 8x $ from both sides:
$ -4y = -8x + 16 $

## Step 2: Solve for $ y $
Divide every term by $ -4 $:
$ y = \frac{-8x}{-4} + \frac{16}{-4} $
$ y = 2x - 4 $

# Answer: Slope-intercept form: $ \boldsymbol{y = 2x - 4} $

### Problem 18: $ 3x - y = 3 $
# Explanation:
## Step 1: Isolate the $ y $-term
Subtract $ 3x $ from both sides:
$ -y = -3x + 3 $

## Step 2: Solve for $ y $
Multiply both sides by $ -1 $:
$ y = 3x - 3 $

# Answer: Slope-intercept form: $ \boldsymbol{y = 3x - 3} $

### Graphing Notes (General):
To graph a line in slope-intercept form ($ y = mx + b $):
1. Plot the $ y $-intercept $ (0, b) $.
2. Use the slope $ m $ (rise over run) to find a second point.
3. Draw a line through the two points.

- For $ y = 4x + 7 $: Plot $ (0, 7) $, then rise $ 4 $, run $ 1 $ (e.g., $ (1, 11) $).
- For $ y = -x + 2 $: Plot $ (0, 2) $, then rise $ -1 $, run $ 1 $ (e.g., $ (1, 1) $).
- For $ y = -\frac{3}{4}x - 4 $: Plot $ (0, -4) $, then rise $ -3 $, run $ 4 $ (e.g., $ (4, -7) $).
- For $ y = \frac{1}{2}x $: Plot $ (0, 0) $, then rise $ 1 $, run $ 2 $ (e.g., $ (2, 1) $).
- For $ y = 2x - 4 $: Plot $ (0, -4) $, then rise $ 2 $, run $ 1 $ (e.g., $ (1, -2) $).
- For $ y = 3x - 3 $: Plot $ (0, -3) $, then rise $ 3 $, run $ 1 $ (e.g., $ (1, 0) $).

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QUESTION IMAGE

Question

Explanation:

Problem 13: \( 8x - 2y = -14 \)

Step 1: Isolate the \( y \)-term

Step 2: Solve for \( y \)

Step 1: Isolate \( y \)

Step 1: Isolate the \( y \)-term

Step 2: Solve for \( y \)

Answer:

Problem 14: \( x + y = 2 \)