Let’s solve the worksheet step by step.
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Part 1: Questions 1–6 — Identify the slope and y-intercept
We use the
slope-intercept form of a line:
>
y = mx + b
Where:
-
m = slope
-
b = y-intercept (the y-value when x = 0)
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1. y = 5x – 1
- Slope (
m) =
5
- y-int (
b) =
–1
✔ Answer:
- Slope:
5
- y-int:
–1
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2. y = –3x
This is the same as
y = –3x + 0
- Slope (
m) =
–3
- y-int (
b) =
0
✔ Answer:
- Slope:
–3
- y-int:
0
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3. y = x – 4
Same as
y = 1x – 4
- Slope (
m) =
1
- y-int (
b) =
–4
✔ Answer:
- Slope:
1
- y-int:
–4
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4. y = 7 – (1/3)x
Rewrite in standard slope-intercept form:
y = –(1/3)x + 7
- Slope (
m) =
–1/3
- y-int (
b) =
7
✔ Answer:
- Slope:
–1/3
- y-int:
7
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5. y = –x
Same as
y = –1x + 0
- Slope (
m) =
–1
- y-int (
b) =
0
✔ Answer:
- Slope:
–1
- y-int:
0
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6. y = (4/3) – 8x
Rewrite:
y = –8x + 4/3
- Slope (
m) =
–8
- y-int (
b) =
4/3
✔ Answer:
- Slope:
–8
- y-int:
4/3
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##
Part 2: Questions 7 & 8 — Write the equation from the graph
We use the same
y = mx + b form. We need to find
slope (m) and
y-intercept (b) from the graph.
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Question 7: Graph on left
Look at the graph:
- The line crosses the
y-axis at (0, –3) → so
b = –3
- To find slope, pick two points:
- From (0, –3), go to (3, 3) — that’s up 6, right 3 → rise/run = 6/3 =
2
- So
m = 2
Equation:
y = 2x – 3
✔ Answer:
y = 2x – 3
*(Check jumbled answers — yes, “y = 2x – 3” is there)*
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Question 8: Graph on right
Look at the graph:
- Crosses y-axis at
(0, 3) → so
b = 3
- Pick another point: goes to (4, –1)
- From (0, 3) to (4, –1): down 4, right 4 → rise/run = –4/4 =
–1
- So
m = –1
Equation:
y = –1x + 3 or
y = –x + 3
But wait — look at the jumbled answers provided:
> Jumbled Answers:
> 0, –8, 7, –3, 5, 1, –1, –1, –1/3, 4/3, –4
> Equations:
> y = (2/3)x + 1
> y = (–3/4)x + 3
> y = –4x – 2
Our calculated equation
y = –x + 3 is
not listed.
Wait — let’s double-check the graph for Question 8.
Looking more carefully:
The line goes through:
- (0, 3) — y-intercept
✔
- Let’s check point (4, –1) again? Actually, looking at the grid, it might be going through (3, 0) or (4, –1)? Let’s count:
From (0, 3):
- Move right 4 units → x=4
- Down 3 units → y=0? Wait, no — at x=4, y is
–1, so change in y = –4, change in x = 4 → slope = –1.
But none of the jumbled equations match
y = –x + 3.
Wait — perhaps I misread the graph?
Alternative: Maybe the line passes through (0, 3) and (4, 0)?
If it goes from (0,3) to (4,0):
- Δy = 0 – 3 = –3
- Δx = 4 – 0 = 4
- Slope = –3/4
Then equation:
y = (–3/4)x + 3
✔ And that
IS one of the jumbled answers!
So likely, the point at x=4 is
y=0, not y=–1 — maybe the graph is drawn with the line passing through (4,0).
Let’s verify:
At x=0 → y=3
At x=4 → y=0 → slope = (0–3)/(4–0) = –3/4 → correct.
So the equation is:
y = –(3/4)x + 3
✔ Answer:
y = –(3/4)x + 3
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✔ Final Answers:
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Questions 1–6:
1. Slope:
5, y-int:
–1
2. Slope:
–3, y-int:
0
3. Slope:
1, y-int:
–4
4. Slope:
–1/3, y-int:
7
5. Slope:
–1, y-int:
0
6. Slope:
–8, y-int:
4/3
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Questions 7 & 8:
7. Equation:
y = 2x – 3
8. Equation:
y = –(3/4)x + 3
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Let me know if you’d like me to explain how to graph any of these too!
Parent Tip: Review the logic above to help your child master the concept of slopes and intercepts worksheet answers.
