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

It looks like you've uploaded a math worksheet focused on linear equations, specifically involving slope, intercepts, and writing equations in slope-intercept form ($ y = mx + b $). Since I can't view images directly, I’ll guide you through solving the types of problems typically found on such a worksheet based on your description.

Let’s go step-by-step through the common tasks in this type of worksheet:

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Problem 1: Find the slope between two points

Given two points, use the slope formula:
$$
m = \frac{y_2 - y_1}{x_2 - x_1}
$$

#### Example:
a. (5, 9) and (5, 1)
- $ x_1 = 5, y_1 = 9 $
- $ x_2 = 5, y_2 = 1 $
- $ m = \frac{1 - 9}{5 - 5} = \frac{-8}{0} $ → undefined slope (vertical line)

b. (-4, 4) and (-4, 9)
- Same $ x $-values → vertical line → undefined slope

> ✔ Answer: Both have undefined slopes (vertical lines).

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Problem 2: Write the equation of the line in SLOPE-INTERCEPT FORM

You’re given graphs of lines. To find $ y = mx + b $, do the following:

1. Find the slope ($ m $): Pick two points on the line and use the slope formula.
2. Find the y-intercept ($ b $): Where the line crosses the $ y $-axis.
3. Plug into $ y = mx + b $.

#### Example Graph:
Suppose a line passes through (0, 2) and (2, 6):

- Slope: $ m = \frac{6 - 2}{2 - 0} = \frac{4}{2} = 2 $
- Y-intercept: $ b = 2 $ (since it crosses $ y $-axis at (0,2))
- Equation: $ y = 2x + 2 $

Repeat for each graph.

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Problem 3: Identify slope and y-intercept from an equation

Given an equation, rewrite in slope-intercept form if needed.

#### Examples:
a. $ y = 4x - 3 $
- Already in slope-intercept form
- $ m = 4 $, $ b = -3 $

b. $ y = -\frac{1}{2}x + 5 $
- $ m = -\frac{1}{2} $, $ b = 5 $

c. $ 6 = \frac{2}{3}x + y $ → Solve for $ y $:
$$
y = -\frac{2}{3}x + 6
$$
- $ m = -\frac{2}{3} $, $ b = 6 $

d. $ \frac{1}{2} = -x + y $ → $ y = x + \frac{1}{2} $
- $ m = 1 $, $ b = \frac{1}{2} $

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Problem 4: Find the equation in slope-intercept form

You might be given two points or a point and a slope.

#### Example:
Find the equation of the line passing through (2, 3) with slope $ m = 2 $.

Use point-slope form:
$$
y - y_1 = m(x - x_1)
$$
$$
y - 3 = 2(x - 2)
$$
$$
y - 3 = 2x - 4
$$
$$
y = 2x - 1
$$

✔ Final answer: $ y = 2x - 1 $

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Summary of Key Concepts:

- Slope-intercept form: $ y = mx + b $
- Slope formula: $ m = \frac{y_2 - y_1}{x_2 - x_1} $
- Vertical lines: undefined slope, equation is $ x = a $
- Horizontal lines: slope = 0, equation is $ y = b $
- Always identify $ m $ and $ b $ to write the equation.

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If you can describe the specific graphs or equations from the image (e.g., coordinates of points, where lines cross axes), I can give exact answers for each problem.

Let me know what you'd like clarified!