Ch 3 - Proportional Relationships & Slope

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Questions and Answers

What is a linear relationship?

  • A relationship that varies non-linearly
  • A relationship that has a curved graph
  • A relationship of three or more quantities
  • A relationship of two quantities that has a straight line graph (correct)

What is the constant rate of change in a linear relationship?

The rate of change between any two points is the same or constant.

Define unit rate.

A rate or ratio with a denominator of 1.

What does the slope represent?

<p>The rate of change between any two points on a line.</p> Signup and view all the answers

What does 'rise' refer to in a linear relationship?

<p>The vertical change between any two points on a line.</p> Signup and view all the answers

What does 'run' refer to in a linear relationship?

<p>The horizontal change between any two points on a line.</p> Signup and view all the answers

What is direct variation?

<p>A relationship between two variable quantities with a constant ratio.</p> Signup and view all the answers

What is the constant of variation?

<p>A constant ratio in a direct variation.</p> Signup and view all the answers

What is the constant of proportionality?

<p>The constant ratio in a proportional linear relationship.</p> Signup and view all the answers

What is point-slope form?

<p>An equation in the form of y - y1 = m(x - x1), where m is the slope and (x1, y1) is any point on a non-vertical line.</p> Signup and view all the answers

What is slope-intercept form?

<p>An equation written in y = mx + b form, where m is the slope and b is the y-intercept.</p> Signup and view all the answers

What is standard form?

<p>An equation written in Ax + By = C form.</p> Signup and view all the answers

What does x-intercept refer to?

<p>The x-coordinate of the point where the line crosses the x-axis.</p> Signup and view all the answers

What does y-intercept refer to?

<p>The y-coordinate of the point where the line crosses the y-axis.</p> Signup and view all the answers

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Study Notes

Linear Relationships

  • Represented graphically by a straight line indicating a constant relationship between two quantities.

Constant Rate of Change

  • The change between any two points in a linear relationship remains the same across the graph.

Unit Rate

  • A specific type of rate or ratio where the denominator equals one, simplifying comparisons.

Slope

  • Measures the steepness of a line, defined as the ratio of vertical change (rise) to horizontal change (run).

Rise

  • The vertical distance between any two points on the line, indicating how much the y-value changes.

Run

  • The horizontal distance between two points on the line, indicating how much the x-value changes.

Direct Variation

  • Describes a relationship where two variable quantities maintain a consistent ratio.

Constant of Variation

  • The constant ratio found within a direct variation, signifying the relationship strength.

Constant of Proportionality

  • The constant ratio in proportional linear relationships, symbolizing direct proportionality between variables.

Point-Slope Form

  • Form of linear equation expressed as y - y1 = m(x - x1), where m indicates slope and (x1, y1) is a specific point on the line.

Slope-Intercept Form

  • Linear equation format written as y = mx + b, where m represents slope and b represents the y-coordinate where the line intersects the y-axis.

Standard Form

  • Linear equations structured as Ax + By = C, where A, B, and C are constants.

x-intercept

  • The specific x-coordinate at which the line intersects the x-axis, determined by setting y to zero in the equation.

y-intercept

  • The specific y-coordinate at which the line intersects the y-axis, determined by setting x to zero in the equation.

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