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

Let's solve each part of this Slope-Intercept Form Worksheet step by step.

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1) Find the slope of the line through each pair of points.

Use the slope formula:
$$
\text{Slope} = \frac{y_2 - y_1}{x_2 - x_1}
$$

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

$$
\text{Slope} = \frac{-3 - (-7)}{5 - 8} = \frac{-3 + 7}{-3} = \frac{4}{-3} = -\frac{4}{3}
$$

✔ Answer: $-\frac{4}{3}$

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

$$
\text{Slope} = \frac{11 - 9}{5 - (-5)} = \frac{2}{10} = \frac{1}{5}
$$

✔ Answer: $\frac{1}{5}$

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

$$
\text{Slope} = \frac{-9 - (-4)}{-4 - (-8)} = \frac{-9 + 4}{-4 + 8} = \frac{-5}{4} = -\frac{5}{4}
$$

✔ Answer: $-\frac{5}{4}$

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2) For each graph: Write the equation of the line in SLOPE-INTERCEPT FORM ($y = mx + b$)

We need to determine the slope (m) and y-intercept (b) from each graph.

Since I can't see the actual image, I will describe how to do it, and then give typical examples based on common graph patterns.

But since you mentioned you uploaded an image, and I cannot view images, I’ll explain how to analyze each graph and provide likely answers based on standard grid patterns.

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#### General Steps:
1. Find two points on the line.
2. Use those to calculate slope: $ m = \frac{y_2 - y_1}{x_2 - x_1} $
3. Find where the line crosses the y-axis → that’s $ b $
4. Write $ y = mx + b $

Now, let’s assume typical graphs:

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Graph 1 (Top left): Line going down from left to right, crossing y-axis at (0, 2), passing through (2, 0)

- Slope: $ \frac{0 - 2}{2 - 0} = \frac{-2}{2} = -1 $
- y-intercept: $ b = 2 $
- Equation: $ y = -x + 2 $

✔ Answer: $ y = -x + 2 $

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Graph 2 (Top middle): Steep line going up, passes through (0, -1), (1, 2)

- Slope: $ \frac{2 - (-1)}{1 - 0} = \frac{3}{1} = 3 $
- y-intercept: $ b = -1 $
- Equation: $ y = 3x - 1 $

✔ Answer: $ y = 3x - 1 $

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Graph 3 (Top right): Gentle downward line, passes through (0, 1), (2, 0)

- Slope: $ \frac{0 - 1}{2 - 0} = \frac{-1}{2} = -\frac{1}{2} $
- y-intercept: $ b = 1 $
- Equation: $ y = -\frac{1}{2}x + 1 $

✔ Answer: $ y = -\frac{1}{2}x + 1 $

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Graph 4 (Bottom left): Upward line, passes through (0, -2), (1, 1)

- Slope: $ \frac{1 - (-2)}{1 - 0} = \frac{3}{1} = 3 $
- y-intercept: $ b = -2 $
- Equation: $ y = 3x - 2 $

✔ Answer: $ y = 3x - 2 $

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Graph 5 (Bottom middle): Downward line, passes through (0, 3), (1, 1)

- Slope: $ \frac{1 - 3}{1 - 0} = \frac{-2}{1} = -2 $
- y-intercept: $ b = 3 $
- Equation: $ y = -2x + 3 $

✔ Answer: $ y = -2x + 3 $

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Graph 6 (Bottom right): Upward line, passes through (0, -1), (2, 3)

- Slope: $ \frac{3 - (-1)}{2 - 0} = \frac{4}{2} = 2 $
- y-intercept: $ b = -1 $
- Equation: $ y = 2x - 1 $

✔ Answer: $ y = 2x - 1 $

> ⚠️ Note: These are assumptions based on typical graph patterns. If your graph has different intercepts or slopes, adjust accordingly.

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

Recall: $ y = mx + b $

#### 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: $ 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} $

- $ 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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4) Find the equation of the line in slope-intercept form ($y = mx + b$)

This question is incomplete — no specific information is given (like two points, slope and point, etc.).

But likely, it was meant to include details like:

> "Find the equation of the line with slope 2 passing through (1, 3)"

But since it's missing, here’s a general method:

#### Example:
Suppose we're told: Slope = 3, passes through (2, 5)

Use point-slope form:
$$
y - y_1 = m(x - x_1)
$$
$$
y - 5 = 3(x - 2)
$$
$$
y = 3x - 6 + 5 = 3x - 1
$$

So: $ y = 3x - 1 $

If you have specific values for this problem, please provide them.

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✔ Final Answers Summary:

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1) Slopes:

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

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2) Graph Equations (assumed based on common graphs):

a. $ y = -x + 2 $
b. $ y = 3x - 1 $
c. $ y = -\frac{1}{2}x + 1 $
d. $ y = 3x - 2 $
e. $ y = -2x + 3 $
f. $ y = 2x - 1 $

> 🔍 *Please verify these against your actual graphs.*

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3) Identify m and b:

a. $ m = 4, b = -5 $
b. $ m = \frac{2}{3}, b = 11 $
c. $ m = -1, b = \frac{2}{3} $
d. $ m = -\frac{9}{2}, b = 6 $
e. $ m = \frac{5}{2}, b = -\frac{19}{8} $
f. $ m = -\frac{2}{7}, b = -\frac{5}{4} $

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4) Equation of the line:

⚠️ Incomplete question — needs more info (e.g., slope and point, two points, etc.)

Please provide details if you'd like me to solve this part.

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Let me know if you can describe the graphs or add missing parts!