Linear Relationships - 4 Corners Activity

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 a linear equation of the form 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 the dependent variable (y) with respect to the independent variable (x). It indicates how steep the line is and the direction it goes (positive or negative).

Front

What is the y-intercept in a linear equation?

Back

The y-intercept is the point where the line crosses the y-axis. It is the value of y when x is 0, represented by the 'b' in the equation y = mx + b.

Front

How do you identify a slope from a graph?

Back

To identify the slope from a graph, choose two points on the line, calculate the rise (change in y) and run (change in x) between these points, and then divide rise by run (slope = rise/run).

Front

What is the difference between a table and a graph in representing linear relationships?

Back

A table lists pairs of values (x, y) that represent the relationship, while a graph visually displays these pairs as points on a coordinate plane, showing the overall trend.

Front

What does it mean if a line has a negative slope?

Back

A negative slope indicates that as the value of x increases, the value of y decreases. The line slopes downward from left to right.

Front

What is the equation of a line with a slope of 2 and a y-intercept of -3?

Back

The equation of the line is y = 2x - 3.

Front

How can you determine if a point lies on a line represented by an equation?

Back

To determine if a point (x, y) lies on a line, substitute the x-value into the equation and see if the resulting y-value matches the y-value of the point.

Front

What is the purpose of using a graph to represent data?

Back

Graphs help visualize relationships between variables, making it easier to identify trends, patterns, and outliers in the data.

Front

What does it mean for two lines to be parallel?

Back

Two lines are parallel if they have the same slope but different y-intercepts, meaning they will never intersect.