scatter plots: line of best fit
write the slope-intercept form equation of the trend line of each scatter plot.
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equation of the trend line:
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equation of the trend line:
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equation of the trend line:
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equation of the trend line:
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equation of the trend line:
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equation of the trend line:
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equation of the trend line:
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equation of the trend line:
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equation of the trend line:

Question

Accepted Answer

### Problem 1 (First Scatter Plot)
# Explanation:
## Step1: Identify two points on the line
From the graph, the line passes through $(0, 9)$ (y-intercept) and let's take another point, say $(10, 6)$.

## Step2: Calculate the slope ($m$)
The slope formula is $m=\frac{y_2 - y_1}{x_2 - x_1}$. Using $(0, 9)$ as $(x_1,y_1)$ and $(10, 6)$ as $(x_2,y_2)$, we get $m=\frac{6 - 9}{10 - 0}=\frac{-3}{10}=-0.3$.

## Step3: Write the slope - intercept form ($y = mx + b$)
We know $b = 9$ (from the y - intercept $(0,9)$) and $m=-0.3$. So the equation is $y=-0.3x + 9$ or $y =-\frac{3}{10}x+9$.

# Answer:
$y =-\frac{3}{10}x + 9$ (or $y=-0.3x + 9$)

### Problem 2 (Second Scatter Plot)
# Explanation:
## Step1: Identify two points on the line
The line passes through $(0, 10)$ (y - intercept) and $(10, 22)$.

## Step2: Calculate the slope ($m$)
Using the slope formula $m=\frac{y_2 - y_1}{x_2 - x_1}$ with $(x_1,y_1)=(0,10)$ and $(x_2,y_2)=(10,22)$, we have $m=\frac{22 - 10}{10 - 0}=\frac{12}{10}=1.2$ or $\frac{6}{5}$.

## Step3: Write the slope - intercept form
Since $b = 10$ and $m = 1.2$, the equation is $y = 1.2x+10$ or $y=\frac{6}{5}x + 10$.

# Answer:
$y=\frac{6}{5}x + 10$ (or $y = 1.2x+10$)

### Problem 3 (Third Scatter Plot)
# Explanation:
## Step1: Identify two points on the line
The line passes through $(0, 0)$ (y - intercept) and $(25, 35)$ (approximate).

## Step2: Calculate the slope
$m=\frac{35 - 0}{25 - 0}=\frac{35}{25}=\frac{7}{5}=1.4$.

## Step3: Write the slope - intercept form
Since $b = 0$ and $m = 1.4$, the equation is $y = 1.4x$ or $y=\frac{7}{5}x$.

# Answer:
$y=\frac{7}{5}x$ (or $y = 1.4x$)

### Problem 4 (Fourth Scatter Plot)
# Explanation:
## Step1: Identify two points on the line
The line passes through $(0, 8)$ (y - intercept) and $(10, 4)$.

## Step2: Calculate the slope
$m=\frac{4 - 8}{10 - 0}=\frac{-4}{10}=-0.4$ or $-\frac{2}{5}$.

## Step3: Write the slope - intercept form
With $b = 8$ and $m=-0.4$, the equation is $y=-0.4x + 8$ or $y=-\frac{2}{5}x + 8$.

# Answer:
$y=-\frac{2}{5}x + 8$ (or $y=-0.4x + 8$)

### Problem 5 (Fifth Scatter Plot)
# Explanation:
## Step1: Identify two points on the line
The line passes through $(0, 8)$ (y - intercept) and $(40, 1)$ (approximate).

## Step2: Calculate the slope
$m=\frac{1 - 8}{40 - 0}=\frac{-7}{40}=-0.175$ (approximate). A better pair might be $(0, 8)$ and $(40, 0)$ (since the line seems to go to $(40,0)$). Then $m=\frac{0 - 8}{40 - 0}=\frac{-8}{40}=-0.2$ or $-\frac{1}{5}$.

## Step3: Write the slope - intercept form
With $b = 8$ and $m=-0.2$, the equation is $y=-0.2x + 8$ or $y=-\frac{1}{5}x + 8$.

# Answer:
$y=-\frac{1}{5}x + 8$ (or $y=-0.2x + 8$)

### Problem 6 (Sixth Scatter Plot)
# Explanation:
## Step1: Identify two points on the line
The line passes through $(0, 70)$ (y - intercept) and $(10, 15)$ (approximate). A better pair: $(0, 70)$ and $(10, 10)$ (approximate). Then $m=\frac{10 - 70}{10 - 0}=\frac{-60}{10}=-6$. Wait, maybe $(0, 70)$ and $(9, 15)$ (approximate). Wait, looking at the graph, the line goes from $(0,70)$ to $(10,10)$ (approximate). So $m=\frac{10 - 70}{10 - 0}=-6$? No, maybe a better approach. Let's take $(0, 70)$ and $(5, 40)$. Then $m=\frac{40 - 70}{5 - 0}=\frac{-30}{5}=-6$? No, that can't be. Wait, maybe the y - intercept is $(0,70)$ and another point $(10,10)$. Then $m=\frac{10 - 70}{10}=-6$. But let's check again. Alternatively, if the line goes from $(0,70)$ to $(10,10)$, the equation is $y=-6x + 70$? Wait, no, maybe I made a mistake. Let's take two clear points. Let's say $(0,70)$ and $(5,40)$. Then $m=\frac{40 - 70}{5}=-6$. So the equation is $y=-6x + 70$? Wait, but when $x = 0$, $y = 70$, and when $x = 5$, $y=-6\times5 + 70=-30 + 70 = 40$, which matches. So the equation is $y=-6x + 70$ (approximate, depending on the exact points).

# Answer:
$y=-6x + 70$ (approximate, may vary slightly based on point selection)

### Problem 7 (Seventh Scatter Plot)
# Explanation:
## Step1: Identify two points on the line
The line passes through $(0, 0)$ (y - intercept) and $(5, 8)$ (approximate).

## Step2: Calculate the slope
$m=\frac{8 - 0}{5 - 0}=\frac{8}{5}=1.6$.

## Step3: Write the slope - intercept form
Since $b = 0$ and $m = 1.6$, the equation is $y = 1.6x$ or $y=\frac{8}{5}x$.

# Answer:
$y=\frac{8}{5}x$ (or $y = 1.6x$)

### Problem 8 (Eighth Scatter Plot)
# Explanation:
## Step1: Identify two points on the line
The line passes through $(0, 30)$ (y - intercept) and $(10, 20)$ (approximate).

## Step2: Calculate the slope
$m=\frac{20 - 30}{10 - 0}=\frac{-10}{10}=-1$. Wait, a better pair: $(0, 30)$ and $(5, 25)$. Then $m=\frac{25 - 30}{5 - 0}=-1$.

## Step3: Write the slope - intercept form
Since $b = 30$ and $m=-1$, the equation is $y=-x + 30$.

# Answer:
$y=-x + 30$

### Problem 9 (Ninth Scatter Plot)
# Explanation:
## Step1: Identify two points on the line
The line passes through $(0, 30)$ (y - intercept) and $(40, 50)$ (approximate).

## Step2: Calculate the slope
$m=\frac{50 - 30}{40 - 0}=\frac{20}{40}=\frac{1}{2}=0.5$.

## Step3: Write the slope - intercept form
Since $b = 30$ and $m = 0.5$, the equation is $y = 0.5x+30$ or $y=\frac{1}{2}x + 30$.

# Answer:
$y=\frac{1}{2}x + 30$ (or $y = 0.5x+30$)

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QUESTION IMAGE

Question

Explanation:

Problem 1 (First Scatter Plot)

Step1: Identify two points on the line

Step2: Calculate the slope (\(m\))

Step3: Write the slope - intercept form (\(y = mx + b\))

Step1: Identify two points on the line

Step2: Calculate the slope (\(m\))

Step3: Write the slope - intercept form

Step1: Identify two points on the line

Step2: Calculate the slope

Step3: Write the slope - intercept form

Answer:

Problem 2 (Second Scatter Plot)