Slope and Slope Intercept Form Worksheet | PDF | Equations ... - Free Printable

Thank you for uploading the worksheet. Since I can’t see the actual image (as this platform doesn’t support image uploads or visual analysis), I’ll solve all the problems based on the text you provided, which appears to be a complete worksheet on slope-intercept form.

I’ll go problem by problem, with full explanations.

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## ✔ Problem 1: Find the slope of the line through each pair of points.

Formula:
> Slope = \( m = \frac{y_2 - y_1}{x_2 - x_1} \)

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a. (8, -7) and (5, -3)

Let’s label:
- \( (x_1, y_1) = (8, -7) \)
- \( (x_2, y_2) = (5, -3) \)

\[
m = \frac{-3 - (-7)}{5 - 8} = \frac{-3 + 7}{-3} = \frac{4}{-3} = -\frac{4}{3}
\]

✔ Answer: \( -\frac{4}{3} \)

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b. (-5, 9) and (5, 11)

Label:
- \( (x_1, y_1) = (-5, 9) \)
- \( (x_2, y_2) = (5, 11) \)

\[
m = \frac{11 - 9}{5 - (-5)} = \frac{2}{10} = \frac{1}{5}
\]

✔ Answer: \( \frac{1}{5} \)

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c. (-8, -4) and (-4, -9)

Label:
- \( (x_1, y_1) = (-8, -4) \)
- \( (x_2, y_2) = (-4, -9) \)

\[
m = \frac{-9 - (-4)}{-4 - (-8)} = \frac{-9 + 4}{-4 + 8} = \frac{-5}{4} = -\frac{5}{4}
\]

✔ Answer: \( -\frac{5}{4} \)

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## ✔ Problem 2: For each graph — Write the equation in SLOPE-INTERCEPT FORM

Since I can’t see the graphs, I’ll explain how to do it so you can apply it to your graphs.

Slope-Intercept Form:
> \( y = mx + b \)

Where:
- \( m \) = slope
- \( b \) = y-intercept (where line crosses y-axis)

Steps to find equation from a graph:

1. Find the y-intercept (b): Look where the line crosses the y-axis. That’s your “b”.
2. Find the slope (m): Pick two clear points on the line. Use rise over run:
\( m = \frac{\text{change in } y}{\text{change in } x} \)
3. Plug into \( y = mx + b \).

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⚠️ Since no graphs are visible, I cannot give specific equations. But here’s how you’d approach each one:

#### Example for Graph 1 (top left):
Suppose the line crosses y-axis at (0, 2) → so b = 2.
From (0,2) to (2, 1) → down 1, right 2 → slope = -1/2
→ Equation: \( y = -\frac{1}{2}x + 2 \)

You must do this for each of the 6 graphs using their actual grid points.

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## ✔ Problem 3: In each linear equation, identify the slope (m) and the y-intercept (b)

Recall: In \( y = mx + b \),
→ m is the coefficient of x
→ b is the constant term

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a. \( y = 4x - 5 \)

→ m = 4
→ b = -5

✔ Answer: m = 4, b = -5

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b. \( y = 11 + \frac{2}{3}x \)

Rewrite as: \( y = \frac{2}{3}x + 11 \)

→ m = \( \frac{2}{3} \)
→ b = 11

✔ Answer: m = \( \frac{2}{3} \), b = 11

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c. \( y = \frac{2}{3} - x \)

Rewrite: \( y = -x + \frac{2}{3} \)

→ m = -1
→ b = \( \frac{2}{3} \)

✔ Answer: m = -1, b = \( \frac{2}{3} \)

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d. \( 6 - \frac{9}{2}x = y \)

Rewrite: \( y = -\frac{9}{2}x + 6 \)

→ m = \( -\frac{9}{2} \)
→ b = 6

✔ Answer: m = \( -\frac{9}{2} \), b = 6

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e. \( y = \frac{5}{2}x - \frac{19}{8} \)

Already in form.

→ m = \( \frac{5}{2} \)
→ b = \( -\frac{19}{8} \)

✔ Answer: m = \( \frac{5}{2} \), b = \( -\frac{19}{8} \)

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f. \( -\frac{5}{4} - \frac{2}{7}x = y \)

Rewrite: \( y = -\frac{2}{7}x - \frac{5}{4} \)

→ m = \( -\frac{2}{7} \)
→ b = \( -\frac{5}{4} \)

✔ Answer: m = \( -\frac{2}{7} \), b = \( -\frac{5}{4} \)

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## ✔ Problem 4: Find the equation of the line in slope-intercept form (y = mx + b)

⚠️ This problem is incomplete in your text — it says “Find the equation…” but gives no points, slope, or graph.

This might be an error — perhaps you meant to include more info? Or maybe it refers to the graphs in Problem 2?

If this is meant to be solved using the graphs from Problem 2, then refer back to those.

Alternatively, if you have additional data (like two points or slope and intercept), please provide it!

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## 📌 Summary of Answers:

Problem 1:

a. \( -\frac{4}{3} \)
b. \( \frac{1}{5} \)
c. \( -\frac{5}{4} \)

Problem 2:

*(Cannot solve without graphs — follow steps above)*

Problem 3:

a. m=4, b=-5
b. m=2/3, b=11
c. m=-1, b=2/3
d. m=-9/2, b=6
e. m=5/2, b=-19/8
f. m=-2/7, b=-5/4

Problem 4:

*(Incomplete — needs more info)*

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## 💡 Tips for Problem 2 (Graphs):

- Always start by finding where the line crosses the y-axis — that’s your b.
- Then pick two points with whole number coordinates.
- Count rise (vertical change) and run (horizontal change).
- Slope = rise/run → reduce fraction if needed.
- Plug into \( y = mx + b \).

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If you can describe the graphs (e.g., “Line goes through (0,3) and (2,1)”), I can help write the equations! Just paste the details.

Otherwise, you’re all set for Problems 1 and 3 — and now you know how to tackle Problem 2! 😊