Proportional and Linear Relationships Quiz

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Questions and Answers

What is a proportional relationship?

  • A relationship where the ratio of one quantity to the other is constant (correct)
  • A relationship that is represented by a straight line on a graph
  • A relationship that can be expressed in the form y = mx + b
  • A relationship that does not pass through the origin

What defines a non-proportional relationship?

  • The line passes through the origin
  • The relationship is proportional
  • There is a constant rate of change
  • It can be expressed as y = mx + b where b is not 0 (correct)

What is a rate?

A ratio of two quantities measured in different units.

What is a unit rate?

<p>A rate in which the second quantity is one unit.</p> Signup and view all the answers

What does a linear relationship represent?

<p>A change in the independent variable causes a proportionally equal change in the dependent variable.</p> Signup and view all the answers

What is the constant of proportionality?

<p>In a proportional relationship, it is the constant value of the ratio of two quantities.</p> Signup and view all the answers

What is a proportion?

<p>An equation stating that two ratios are equal.</p> Signup and view all the answers

What is a constant?

<p>A value that does not change.</p> Signup and view all the answers

What is direct variation?

<p>Increase in one variable causes a proportional increase in another variable.</p> Signup and view all the answers

What is the slope?

<p>The steepness of a line on a graph.</p> Signup and view all the answers

What does 'change in y values' refer to?

<p>The difference in the change of the y values in a table (y2 - y1).</p> Signup and view all the answers

What does 'change in x values' refer to?

<p>The difference in the change of the x values in a table (x2 - x1).</p> Signup and view all the answers

What is the rate of change?

<p>A ratio that compares the amount of change in a dependent variable to the amount of change in an independent variable.</p> Signup and view all the answers

What does linear mean in mathematics?

<p>A relationship or function that can be represented by a straight line.</p> Signup and view all the answers

What is the delta symbol for change?

<p>Δ</p> Signup and view all the answers

What does Δy / Δx represent?

<p>Change in the y values divided by the change in the x values.</p> Signup and view all the answers

What is the origin in a coordinate plane?

<p>(0,0)</p> Signup and view all the answers

What is the y-intercept?

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

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Study Notes

Proportional Relationships

  • Defined as a relationship where the ratio between two quantities remains constant.
  • Typically represented by the equation ( y = kx ), where ( k ) is the constant of proportionality.

Non-Proportional Relationships

  • Expressed in the form ( y = mx + b ) with ( b \neq 0 ).
  • The graph is a straight line that does not intersect the origin.

Rate and Unit Rate

  • A rate compares two quantities with different units.
  • A unit rate compares to one unit of the second quantity, often expressed as "per".

Linear Relationships

  • Changes in the independent variable ( x ) result in equal proportional changes in the dependent variable ( y ).
  • Always represented by straight line graphs in the form ( y = mx + b ).

Constant of Proportionality

  • The fixed ratio in a proportional relationship typically written as ( y = kx ).

Proportion

  • An equation indicating that two ratios are equivalent.

Constants

  • Values that remain unchanged in the context of a relationship.

Direct Variation

  • Describes how an increase or decrease in one variable proportionally affects another variable, shown as ( y = kx ).

Slope

  • Represents the steepness of a line on a graph, calculated as the ratio of the change in ( y ) values to the change in ( x ) values (( \text{slope} = \frac{\Delta y}{\Delta x} )).

Change in Values

  • Change in ( y ) values is calculated as ( y_2 - y_1 ).
  • Change in ( x ) values is calculated as ( x_2 - x_1 ).

Rate of Change

  • The ratio comparing the change in a dependent variable to the change in an independent variable, synonymous with slope.

Linear Function

  • A linear relationship or function can be depicted by a straight line on a graph.

Delta Symbol (Δ)

  • Represents change or difference, simplifying the description of variations in values.

Coordinate System

  • The origin is the point where the x-axis and y-axis meet, located at (0,0).

Y-Intercept

  • The coordinate that represents where a graph intersects the y-axis.

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