Intro to Linear Relationships

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. It can be described by the equation y = mx + b, where m is the slope and b is the y-intercept.

Front

What does the slope of a line represent?

Back

The slope of a line represents the rate of change of y with respect to x. It indicates how much y changes for a unit change in x.

Front

What is the y-intercept?

Back

The y-intercept is the point where the line crosses the y-axis. It is the value of y when x is 0.

Front

How do you find the slope from two points?

Back

The slope (m) can be calculated using the formula m = (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are the coordinates of the two points.

Front

What is the equation of a line in slope-intercept form?

Back

The equation of a line in slope-intercept form is y = mx + b, where m is the slope and b is the y-intercept.

Front

What does it mean if a graph is linear?

Back

If a graph is linear, it means that the relationship between the variables is constant, and it can be represented by a straight line.

Front

What is a proportional relationship?

Back

A proportional relationship is a specific type of linear relationship where the line passes through the origin (0,0), meaning that when x is 0, y is also 0.

Front

How can you determine if a relationship is proportional from a table of values?

Back

A relationship is proportional if the ratio of y to x is constant for all pairs of values in the table.

Front

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

Back

Linear relationships can be represented by a straight line, while non-linear relationships cannot and may involve curves or other shapes.

Front

What does it mean to multiply x by a constant to get y?

Back

It means that y is directly proportional to x, and the constant is the slope of the line that represents their relationship.