## Questions and Answers

What is the slope formula?

y2 - y1 / x2 - x1

A slope is considered rising if it is a positive number.

True

A slope is considered falling if it is a negative number.

True

A slope is vertical if the denominator of the slope fraction is 0.

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A slope is horizontal if it is 0.

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Two lines are considered parallel if their slopes are...

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Two lines are considered perpendicular if their slopes are...

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What steps do you need to follow to find a missing number in a pair of points?

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What is the standard form of a linear equation?

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When finding x in standard form, what should you do?

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When finding y in standard form, what should you do?

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What is the slope-intercept form of a linear equation?

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What is the point-slope form of a linear equation?

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If given a coordinate that is parallel to a given slope equation, what should you do?

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If given a coordinate that is perpendicular to a given slope equation, what should you do?

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When graphing inequalities, what kind of line do you draw if the sign is < or > with a line under it?

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When graphing inequalities, what kind of line do you draw if the sign is < or >?

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What are the steps to graphing an inequality?

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How do you model linear functions?

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## Study Notes

### Slope Concepts

- Slope formula is defined as ((y_2 - y_1) / (x_2 - x_1)).
- A rising slope has a positive value indicating the line slopes upwards from left to right.
- A falling slope has a negative value indicating the line slopes downwards from left to right.
- A vertical slope occurs when the denominator in the slope formula equals zero, representing a line that goes straight up and down.
- A horizontal slope has a value of zero, indicating there is no change in the y-coordinate as x varies.

### Line Relationships

- Two lines are parallel if they have identical slopes.
- Two lines are perpendicular if their slopes are opposite reciprocals, meaning one slope could be expressed as (-1/m) if the other slope is (m).

### Finding Missing Coordinates

- To find a missing coordinate:
- Insert known values into the slope formula.
- Solve for the side of the fraction containing the unknown.
- Multiply the known number by the slope.
- Set the product equal to the other half of the fraction and solve for the unknown.

### Forms of Linear Equations

- Standard form of a linear equation is represented as (Ax + By = C).
- To find (x) from a standard form equation, substitute (0) for (y) and solve.
- To find (y) from a standard form equation, substitute (0) for (x) and solve.

### Equation Formats

- Slope-intercept form is expressed as (y = mx + b), where (m) represents the slope and (b) is the y-intercept.
- Point-slope form is represented as (y - y_1 = m(x - x_1)).

### Parallel and Perpendicular Lines

- To establish a line parallel to a given slope, use the given slope and any point in point-slope form.
- To establish a line perpendicular to a given slope, use the opposite reciprocal of the slope from the given line and apply any point in point-slope form.

### Graphing Inequalities

- When graphing inequalities:
- Use a solid line if the inequality sign includes an equal to (≤ or ≥).
- Use a dotted line if the inequality is strict (< or >).

- Steps for graphing an inequality:
- Graph the corresponding line.
- Choose a test point to substitute into the inequality.
- Solve the inequality with the chosen coordinates.
- If the result is true, shade the region of the graph corresponding to the test point.

### Modeling Linear Functions

- Model linear functions by identifying time and numeric conditions relevant to the scenario.
- Represent these conditions as coordinates.
- Use the coordinates to formulate the problem into slope-intercept form and solve accordingly.

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## Description

These flashcards cover key concepts from Unit 1 of Algebra II, focusing on the slope formula and its characteristics. Learn how to identify rising, falling, and vertical slopes through definitions and explanations. Perfect for students preparing for their Algebra II assessments.