Linear Relationships Review

Front

What is a linear relationship?

Back

A linear relationship is a relationship between two variables that can be represented by a straight line on a graph, typically expressed in the form y = mx + b, where m is the slope and b is the y-intercept.

Front

What is the y-intercept in a linear equation?

Back

The y-intercept is the point where the line crosses the y-axis, represented by the value of b in the equation y = mx + b.

Front

What does it mean for a relationship to be proportional?

Back

A proportional relationship is one where the ratio of the two variables remains constant, and it can be represented by the equation y = kx, where k is a constant.

Front

How can you identify a proportional relationship from a set of equations?

Back

A proportional relationship can be identified by checking if the equation passes through the origin (0,0) and if it can be expressed in the form y = kx.

Front

What is the slope of a line, and how is it calculated?

Back

The slope of a line (m) is a measure of its steepness, calculated as the change in y divided by the change in x (rise/run).

Front

What is the difference between proportional and non-proportional relationships?

Back

Proportional relationships have a constant ratio and pass through the origin, while non-proportional relationships do not have a constant ratio and do not pass through the origin.

Front

How do you determine the slope from a word problem involving rates?

Back

To determine the slope from a word problem, identify the rate of change between the two variables, often expressed as 'per unit' (e.g., t-shirts per hour).

Front

What is an example of a non-proportional relationship?

Back

An example of a non-proportional relationship is y = 2x + 3, where the line does not pass through the origin.

Front

What does the term 'rise over run' refer to in the context of slope?

Back

'Rise over run' refers to the vertical change (rise) divided by the horizontal change (run) between two points on a line, used to calculate the slope.

Front

How can you graph a linear equation?

Back

To graph a linear equation, identify the y-intercept, plot it on the graph, and use the slope to find another point, then draw a straight line through the points.