To find the equation of the trend line for each scatter plot, we use the
slope-intercept form:
>
y = mx + b
Where:
-
m is the slope (rise over run)
-
b is the y-intercept (where the line crosses the y-axis)
We’ll go through each graph one by one. Since these are hand-drawn or printed graphs on grid paper, we estimate points that lie *on the trend line* (not necessarily data points) to calculate slope and intercept.
---
Graph ①
Line goes from top-left to bottom-right → negative slope.
Pick two clear points on the line:
Let’s say it passes through (0, 8) and (10, 4).
Slope m = (4 - 8)/(10 - 0) = (-4)/10 =
-0.4
Y-intercept b = 8 (since it crosses y-axis at 8)
→ Equation:
y = -0.4x + 8
But let’s check another point to verify. At x=5, y should be: -0.4(5)+8 = -2+8 = 6 → looks correct on graph.
✔ Final for ①:
y = -0.4x + 8
---
Graph ②
Line goes up to the right → positive slope.
Points: (0, 2) and (10, 7)
m = (7-2)/(10-0) = 5/10 =
0.5
b = 2
→
y = 0.5x + 2
Check: at x=4, y=0.5(4)+2=4 → matches graph.
✔ Final for ②:
y = 0.5x + 2
---
Graph ③
Positive slope. Points: (0, 1) and (10, 6)
m = (6-1)/10 = 5/10 =
0.5
b = 1
→
y = 0.5x + 1
Check: x=2 → y=0.5(2)+1=2 → looks good.
✔ Final for ③:
y = 0.5x + 1
---
Graph ④
Negative slope. Points: (0, 7) and (10, 3)
m = (3-7)/10 = -4/10 =
-0.4
b = 7
→
y = -0.4x + 7
Check: x=5 → y=-2+7=5 → matches.
✔ Final for ④:
y = -0.4x + 7
---
Graph ⑤
Negative slope. Points: (0, 9) and (10, 4)
m = (4-9)/10 = -5/10 =
-0.5
b = 9
→
y = -0.5x + 9
Check: x=2 → y=-1+9=8 → looks right.
✔ Final for ⑤:
y = -0.5x + 9
---
Graph ⑥
Negative slope. Points: (0, 8) and (8, 0) — wait, does it hit (8,0)? Let’s see: if x=8, y=0? Actually, looking again — maybe better to pick (0, 8) and (4, 4).
m = (4-8)/(4-0) = -4/4 =
-1
b = 8
→
y = -x + 8
Check: x=2 → y=6; x=6 → y=2 → yes, fits.
✔ Final for ⑥:
y = -x + 8
---
Graph ⑦
Very flat positive slope. Points: (0, 2) and (10, 3)
m = (3-2)/10 = 1/10 =
0.1
b = 2
→
y = 0.1x + 2
Check: x=5 → y=0.5+2=2.5 → reasonable.
✔ Final for ⑦:
y = 0.1x + 2
---
Graph ⑧
Negative slope. Points: (0, 6) and (10, 4)
m = (4-6)/10 = -2/10 =
-0.2
b = 6
→
y = -0.2x + 6
Check: x=5 → y=-1+6=5 → looks correct.
✔ Final for ⑧:
y = -0.2x + 6
---
Graph ⑨
Positive slope. Points: (0, 1) and (5, 6)
m = (6-1)/5 = 5/5 =
1
b = 1
→
y = x + 1
Check: x=2 → y=3; x=3 → y=4 → perfect.
✔ Final for ⑨:
y = x + 1
---
##
✔ FINAL ANSWERS:
① y = -0.4x + 8
② y = 0.5x + 2
③ y = 0.5x + 1
④ y = -0.4x + 7
⑤ y = -0.5x + 9
⑥ y = -x + 8
⑦ y = 0.1x + 2
⑧ y = -0.2x + 6
⑨ y = x + 1
*(Note: Depending on exact grid interpretation, slight variations like fractions may be acceptable — e.g., -0.4 = -2/5, 0.5 = 1/2 — but decimals are fine unless specified otherwise.)*
Parent Tip: Review the logic above to help your child master the concept of scatter plots worksheet 2 answers.
