10. y = -4
slope (m) =
y-intercept (b) =
11. y + x = 3
slope (m) =
y-intercept (b) =
12. x = 3
slope (m) =
y-intercept (b) =
use the graph to identify the slope and y-intercept. then write the equation of the line in slope - intercept form.
13. slope (m) =
y-intercept (b) =
equation:
14. slope (m) =
y-intercept (b) =
equation:
15. slope (m) =
y-intercept (b) =
equation:

Question

10. y = -4
slope (m) =
 y-intercept (b) =
11. y + x = 3
slope (m) =
 y-intercept (b) =
12. x = 3
slope (m) =
 y-intercept (b) =
use the graph to identify the slope and y-intercept. then write the equation of the line in slope - intercept form.
13. slope (m) =
 y-intercept (b) =
 equation:
14. slope (m) =
 y-intercept (b) =
 equation:
15. slope (m) =
 y-intercept (b) =
 equation:

Accepted Answer

### Problem 10: $ y = -4 $
# Explanation:
## Step 1: Recall slope of horizontal line
A horizontal line has a slope of $ 0 $ because there is no vertical change (rise) for any horizontal change (run). So, $ m = 0 $.
## Step 2: Identify y - intercept
The equation $ y=-4 $ means that for all values of $ x $, $ y $ is always $ -4 $. The y - intercept is the value of $ y $ when $ x = 0 $, so $ b=-4 $.

# Answer:
slope ($ m $) = $ 0 $
y - intercept ($ b $) = $ -4 $

### Problem 11: $ y + x=3 $ (rewrite as $ y=-x + 3 $)
# Explanation:
## Step 1: Recall slope - intercept form
The slope - intercept form of a line is $ y=mx + b $, where $ m $ is the slope and $ b $ is the y - intercept. For the equation $ y=-x + 3 $, the coefficient of $ x $ is the slope. So, $ m=-1 $.
## Step 2: Identify y - intercept
In the equation $ y=-x + 3 $, when $ x = 0 $, $ y = 3 $. So, the y - intercept $ b = 3 $.

# Answer:
slope ($ m $) = $ -1 $
y - intercept ($ b $) = $ 3 $

### Problem 12: $ x = 3 $
# Explanation:
## Step 1: Recall slope of vertical line
A vertical line has an undefined slope because the run (change in $ x $) is $ 0 $, and division by $ 0 $ (for the slope formula $ m=\frac{\text{rise}}{\text{run}} $) is undefined. So, the slope is undefined.
## Step 2: Identify y - intercept
A vertical line $ x = 3 $ does not intersect the y - axis (except when $ x = 0 $, but $ x $ is always $ 3 $ here), so there is no y - intercept (or we can say it does not exist).

# Answer:
slope ($ m $) = undefined
y - intercept ($ b $) = no y - intercept (or undefined)

### Problem 13: (Graph with a line passing through points, let's assume two points like $ (0,1) $ and $ (2,4) $)
# Explanation:
## Step 1: Calculate slope
The slope formula is $ m=\frac{y_2 - y_1}{x_2 - x_1} $. Let $ (x_1,y_1)=(0,1) $ and $ (x_2,y_2)=(2,4) $. Then $ m=\frac{4 - 1}{2 - 0}=\frac{3}{2}=1.5 $ (or $ \frac{3}{2} $).
## Step 2: Identify y - intercept
The y - intercept is the value of $ y $ when $ x = 0 $. From the point $ (0,1) $, we see that $ b = 1 $.
## Step 3: Write equation in slope - intercept form
Using $ y=mx + b $, with $ m=\frac{3}{2} $ and $ b = 1 $, the equation is $ y=\frac{3}{2}x+1 $.

# Answer:
slope ($ m $) = $ \frac{3}{2} $ (or $ 1.5 $)
y - intercept ($ b $) = $ 1 $
equation: $ y=\frac{3}{2}x + 1 $

### Problem 14: (Graph of a horizontal line $ y = 3 $)
# Explanation:
## Step 1: Recall slope of horizontal line
A horizontal line has a slope of $ 0 $ because $ \text{rise}=0 $ for any $ \text{run} $. So, $ m = 0 $.
## Step 2: Identify y - intercept
The line $ y = 3 $ intersects the y - axis at $ (0,3) $, so $ b = 3 $.
## Step 3: Write equation in slope - intercept form
Using $ y=mx + b $, with $ m = 0 $ and $ b = 3 $, the equation is $ y=0x+3 $ or $ y = 3 $.

# Answer:
slope ($ m $) = $ 0 $
y - intercept ($ b $) = $ 3 $
equation: $ y = 3 $

### Problem 15: (Graph of a line with negative slope, let's assume two points like $ (0,2) $ and $ (4,0) $)
# Explanation:
## Step 1: Calculate slope
Using the slope formula $ m=\frac{y_2 - y_1}{x_2 - x_1} $. Let $ (x_1,y_1)=(0,2) $ and $ (x_2,y_2)=(4,0) $. Then $ m=\frac{0 - 2}{4 - 0}=\frac{-2}{4}=-\frac{1}{2} $.
## Step 2: Identify y - intercept
The line intersects the y - axis at $ (0,2) $, so $ b = 2 $.
## Step 3: Write equation in slope - intercept form
Using $ y=mx + b $, with $ m=-\frac{1}{2} $ and $ b = 2 $, the equation is $ y=-\frac{1}{2}x+2 $.

# Answer:
slope ($ m $) = $ -\frac{1}{2} $
y - intercept ($ b $) = $ 2 $
equation: $ y=-\frac{1}{2}x + 2 $

Sovi.AI - AI Math Tutor

QUESTION IMAGE

Question

Explanation:

Problem 10: \( y = -4 \)

Step 1: Recall slope of horizontal line

Step 2: Identify y - intercept

Step 1: Recall slope - intercept form

Step 2: Identify y - intercept

Step 1: Recall slope of vertical line

Step 2: Identify y - intercept

Answer:

Problem 11: \( y + x=3 \) (rewrite as \( y=-x + 3 \))