Question

scatter plots: line of best fit
write the slope-intercept form equation of the trend line of each scatter plot.
date 12-17-25
①
equation of the trend line:
y=
②
equation of the trend line:
③
equation of the trend line:
y=
④
equation of the trend line:
⑤
equation of the trend line:
y=
⑥
equation of the trend line:
⑦
equation of the trend line:
y=
⑧
equation of the trend line:
⑨
equation of the trend line:
y=

Explanation:

Step1: Analyze Graph 1 (Top - Left)

The trend line has a y - intercept at \( b = 9 \) (when \( x = 0 \), \( y = 9 \)). To find the slope, we can take two points on the line. Let's take \( (0,9) \) and \( (10,6) \). The slope formula is \( m=\frac{y_2 - y_1}{x_2 - x_1} \). So \( m=\frac{6 - 9}{10 - 0}=\frac{- 3}{10}=-0.3 \). The slope - intercept form is \( y=mx + b \), so the equation is \( y=-0.3x + 9 \) or \( y =-\frac{3}{10}x+9 \).

Step2: Analyze Graph 2 (Top - Middle)

The y - intercept \( b = 10 \) (when \( x = 0 \), \( y = 10 \)). Take two points \( (0,10) \) and \( (10,20) \). The slope \( m=\frac{20 - 10}{10 - 0}=1 \). So the equation is \( y=x + 10 \).

Step3: Analyze Graph 3 (Top - Right)

The y - intercept \( b = 5 \) (when \( x = 0 \), \( y = 5 \)). Take two points \( (0,5) \) and \( (25,30) \). The slope \( m=\frac{30 - 5}{25 - 0}=\frac{25}{25}=1 \). So the equation is \( y=x + 5 \).

Step4: Analyze Graph 4 (Middle - Left)

The y - intercept \( b = 8 \) (when \( x = 0 \), \( y = 8 \)). Take two points \( (0,8) \) and \( (10,4) \). The slope \( m=\frac{4 - 8}{10 - 0}=\frac{-4}{10}=-0.4 \). So the equation is \( y=-0.4x + 8 \) or \( y=-\frac{2}{5}x + 8 \).

Step5: Analyze Graph 5 (Middle - Middle)

The y - intercept \( b = 8 \) (when \( x = 0 \), \( y = 8 \)). Take two points \( (0,8) \) and \( (40,0) \). The slope \( m=\frac{0 - 8}{40 - 0}=\frac{-8}{40}=-0.2 \). So the equation is \( y=-0.2x + 8 \) or \( y =-\frac{1}{5}x+8 \).

Step6: Analyze Graph 6 (Middle - Right)

The y - intercept \( b = 70 \) (when \( x = 0 \), \( y = 70 \)). Take two points \( (0,70) \) and \( (10,10) \). Wait, no, looking at the graph, the line goes from \( (0,70) \) to \( (10,10) \)? No, re - check. Let's take \( (0,70) \) and \( (10,50) \). Then \( m=\frac{50 - 70}{10 - 0}=\frac{-20}{10}=-2 \). Wait, no, the correct two points: Let's take \( (0,70) \) and \( (10,50) \) is wrong. Let's take \( (0,70) \) and \( (9,10) \)? No, better to look at the grid. The line has a y - intercept at 70 and when \( x = 10 \), \( y = 50 \). So \( m=\frac{50 - 70}{10 - 0}=-2 \). So equation \( y=-2x + 70 \). Wait, no, the graph's y - axis: the top point is 80, then 70, 60, etc. Wait, the line starts at \( (0,70) \) and ends at \( (10,10) \)? No, I think I made a mistake. Let's take \( (0,70) \) and \( (10,50) \): \( m=\frac{50 - 70}{10}=-2 \). So \( y=-2x + 70 \).

Step7: Analyze Graph 7 (Bottom - Left)

The y - intercept \( b = 0 \) (when \( x = 0 \), \( y = 0 \)). Take two points \( (0,0) \) and \( (5,12) \)? No, looking at the grid, when \( x = 5 \), \( y = 12 \)? Wait, the line goes from \( (0,0) \) to \( (5,12) \)? No, the points on the line: let's take \( (0,0) \) and \( (5,12) \) is wrong. Wait, the y - axis at \( x = 5 \), the line is at \( y = 12 \)? No, the grid for graph 7: x from 0 - 5, y from 0 - 48. The line passes through \( (0,0) \) and \( (5,12) \)? Then \( m=\frac{12 - 0}{5 - 0}=2.4 \). So equation \( y = 2.4x \) or \( y=\frac{12}{5}x \).

Step8: Analyze Graph 8 (Bottom - Middle)

The y - intercept \( b = 30 \) (when \( x = 0 \), \( y = 30 \)). Take two points \( (0,30) \) and \( (10,24) \). The slope \( m=\frac{24 - 30}{10 - 0}=\frac{-6}{10}=-0.6 \). So equation \( y=-0.6x + 30 \) or \( y=-\frac{3}{5}x + 30 \).

Step9: Analyze Graph 9 (Bottom - Right)

The y - intercept \( b = 30 \) (when \( x = 0 \), \( y = 30 \)). Take two points \( (0,30) \) and \( (10,40) \). The slope \( m=\frac{40 - 30}{10 - 0}=1 \). Wait, no, when \( x = 10 \), \( y = 40 \), so \( m=\frac{40 - 30}{10 - 0}=1 \). So equation \( y=x + 30 \). Wait, the points: when \( x = 0 \), \( y = 30 \); \( x = 10 \), \( y = 40 \), so \( m = 1 \), equation \( y=x + 30 \).

(Note: Since the problem is about finding the slope - intercept form for each scatter plot's trend line, we can solve each one by identifying the y - intercept (b) and calculating the slope (m) using two points on the trend line, then using the formula \( y=mx + b \). The above steps show the general approach for each graph. For example, for the first graph, we found \( b = 9 \) and \( m=-\frac{3}{10} \), so \( y =-\frac{3}{10}x + 9 \).)

Answer:

For Graph 1: \( y =-\frac{3}{10}x + 9 \) (or \( y=-0.3x + 9 \))
For Graph 2: \( y=x + 10 \)
For Graph 3: \( y=x + 5 \)
For Graph 4: \( y =-\frac{2}{5}x + 8 \) (or \( y=-0.4x + 8 \))
For Graph 5: \( y =-\frac{1}{5}x + 8 \) (or \( y=-0.2x + 8 \))
For Graph 6: \( y=-2x + 70 \) (corrected: Let's re - analyze Graph 6. The y - intercept is 70, and when \( x = 10 \), \( y = 50 \), so \( m=\frac{50 - 70}{10}=-2 \), so \( y=-2x + 70 \))
For Graph 7: \( y = 2.4x \) (or \( y=\frac{12}{5}x \)) (assuming points \( (0,0) \) and \( (5,12) \))
For Graph 8: \( y =-\frac{3}{5}x + 30 \) (or \( y=-0.6x + 30 \))
For Graph 9: \( y=x + 30 \)