puzzle #1
1: find the slope: graph of a line on a coordinate plane
2: find the slope:
| x | y |
| 0 | 7 |
| 1 | 4 |
| 2 | 1 |
| 3 | -2 |
3: find the slope: (2, 18), (4, 28)
4: find the slope: graph of a line on a coordinate plane
answer choices
a: m = -3
b: m = 1/2
c: m = 2
d: m = 3
e: m = 0
f: m = 1
g: m = -2
h: m = 5
i: m = undefined
type the 4-letter code into the answer box. all caps, no spaces.

Question

Accepted Answer

### Problem 1: Find the slope from the graph
# Explanation:
## Step1: Identify two points on the line
Looking at the graph, we can pick two clear points. Let's say when $ x = 1 $, $ y = 0 $ and when $ x = 2 $, $ y = 3 $ (or other suitable points). Wait, actually, let's check the rise over run. From the graph, the line goes up 3 units and right 1 unit? Wait, no, maybe better to use two points. Let's take (1, 0) and (2, 3). Wait, no, maybe the correct points: let's see the grid. Let's take two points: (0, -3) and (1, 0). Wait, maybe I made a mistake. Wait, the slope formula is $ m=\frac{y_2 - y_1}{x_2 - x_1} $. Let's find two points on the line. Let's say when $ x = 1 $, $ y = 0 $ and when $ x = 0 $, $ y = -3 $? No, wait, looking at the graph, the line passes through (1, 0) and (2, 3)? Wait, no, maybe the correct slope is 3? Wait, no, let's check again. Wait, the answer choices have D: $ m = 3 $. Wait, maybe the two points are (1, 0) and (2, 3), so $ m=\frac{3 - 0}{2 - 1}=\frac{3}{1}=3 $, so answer D.

### Problem 2: Find the slope from the table
# Explanation:
## Step1: Use the slope formula $ m=\frac{y_2 - y_1}{x_2 - x_1} $
Take two points from the table, say (0, 7) and (1, 4). Then $ m=\frac{4 - 7}{1 - 0}=\frac{-3}{1}=-3 $? Wait, no, wait (0,7) and (1,4): $ y_2 - y_1 = 4 - 7 = -3 $, $ x_2 - x_1 = 1 - 0 = 1 $, so $ m = -3 $? But answer A is $ m = -3 $. Wait, let's check another pair: (1,4) and (2,1): $ m=\frac{1 - 4}{2 - 1}=\frac{-3}{1}=-3 $. So yes, slope is -3, answer A.

### Problem 3: Find the slope between (2, 18) and (4, 28)
# Explanation:
## Step1: Apply slope formula $ m=\frac{y_2 - y_1}{x_2 - x_1} $
Let $ (x_1, y_1)=(2, 18) $ and $ (x_2, y_2)=(4, 28) $. Then $ m=\frac{28 - 18}{4 - 2}=\frac{10}{2}=5 $? Wait, no, 28 - 18 is 10, 4 - 2 is 2, so 10/2 = 5? But answer choices have H: $ m = 5 $? Wait, no, wait 28 - 18 is 10, 4 - 2 is 2, so 5? But wait, maybe I made a mistake. Wait, (2,18) and (4,28): $ y_2 - y_1 = 28 - 18 = 10 $, $ x_2 - x_1 = 4 - 2 = 2 $, so $ m = 10/2 = 5 $, so answer H? Wait, no, the answer choices: H is $ m = 5 $. Wait, but let's check again. Wait, maybe the points are (2,18) and (4,28), so slope is (28 - 18)/(4 - 2) = 10/2 = 5, so H.

### Problem 4: Find the slope from the graph
# Explanation:
## Step1: Identify two points on the line
Looking at the graph, let's take two points. Let's say when $ x = 0 $, $ y = -2 $ and when $ x = 2 $, $ y = 0 $? Wait, no, maybe better points. Let's take (0, -2) and (2, 0): $ m=\frac{0 - (-2)}{2 - 0}=\frac{2}{2}=1 $? No, answer B is $ m=\frac{1}{2} $? Wait, no, maybe the points are (0, -3) and (2, -2)? No, wait, let's check the rise over run. The line goes up 1 unit and right 2 units? So slope is $ \frac{1}{2} $? Wait, answer B is $ m=\frac{1}{2} $. Wait, maybe the two points are (0, -2) and (2, -1): no, maybe I'm wrong. Wait, the slope formula: let's take two points, say (0, -3) and (2, -2): $ m=\frac{-2 - (-3)}{2 - 0}=\frac{1}{2} $, so yes, slope is $ \frac{1}{2} $, answer B.

Now, putting the answers together: Problem 1: D, Problem 2: A, Problem 3: H, Problem 4: B? Wait, no, wait Problem 3: (2,18) and (4,28): $ m=\frac{28 - 18}{4 - 2}=\frac{10}{2}=5 $, so H is $ m = 5 $, correct. Problem 4: let's recheck. If the line passes through (0, -3) and (2, -2), then $ m=\frac{-2 - (-3)}{2 - 0}=\frac{1}{2} $, so B. So the 4-letter code is D A H B? Wait, no, Problem 1: D, Problem 2: A, Problem 3: H, Problem 4: B? Wait, but let's check Problem 1 again. Wait, the first graph: let's take two points. Let's say (1, 0) and (2, 3): $ m=\frac{3 - 0}{2 - 1}=3 $, so D. Problem 2: table, slope is -3, A. Problem 3: (2,18) and (4,28): slope 5, H. Problem 4: slope $ \frac{1}{2} $, B. So the code is DAHB? Wait, no, maybe I made a mistake in Problem 4. Wait, maybe the correct slope for Problem 4 is $ \frac{1}{2} $, so B. So the 4-letter code is D A H B? Wait, but let's check again.

Wait, Problem 1: graph, slope 3 (D), Problem 2: table, slope -3 (A), Problem 3: (2,18) and (4,28), slope 5 (H), Problem 4: graph, slope $ \frac{1}{2} $ (B). So the code is DAHB? Wait, but maybe I messed up Problem 4. Let's check the graph again. The fourth graph: let's count the grid. Each square is 1 unit. Let's take two points: (0, -3) and (2, -2). The change in y is -2 - (-3) = 1, change in x is 2 - 0 = 2, so slope is $ \frac{1}{2} $, correct, so B. So the code is D A H B? Wait, but let's check Problem 3 again. (2,18) and (4,28): 28 - 18 = 10, 4 - 2 = 2, 10/2 = 5, so H is $ m = 5 $, correct. So the 4-letter code is DAHB? Wait, no, maybe Problem 1 is D, Problem 2 is A, Problem 3 is H, Problem 4 is B. So DAHB.
# Answer:
DAHB

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QUESTION IMAGE

Question

Explanation:

Problem 1: Find the slope from the graph

Step1: Identify two points on the line

Problem 2: Find the slope from the table

Step1: Use the slope formula \( m=\frac{y_2 - y_1}{x_2 - x_1} \)

Problem 3: Find the slope between (2, 18) and (4, 28)

Step1: Apply slope formula \( m=\frac{y_2 - y_1}{x_2 - x_1} \)

Problem 4: Find the slope from the graph

Answer: