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 expressed in the form of an 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 the dependent variable (y) with respect to the independent variable (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 between two points (x1, y1) and (x2, y2)?

Back

The slope (m) can be calculated using the formula: m = (y2 - y1) / (x2 - x1).

Front

What does a positive slope indicate about a linear relationship?

Back

A positive slope indicates that as the independent variable (x) increases, the dependent variable (y) also increases, showing a positive correlation.

Front

What does a negative slope indicate about a linear relationship?

Back

A negative slope indicates that as the independent variable (x) increases, the dependent variable (y) decreases, showing a negative correlation.

Front

What is the formula for the slope-intercept form of a linear equation?

Back

The slope-intercept form of a linear equation is given by: y = mx + b, where m is the slope and b is the y-intercept.

Front

What does the point (x, y) represent on a graph?

Back

The point (x, y) represents a specific location on the Cartesian plane, where x is the value on the horizontal axis and y is the value on the vertical axis.

Front

How can you determine if a graph has a positive or negative growth?

Back

You can determine the growth by observing the direction of the line: if it rises from left to right, it has positive growth; if it falls from left to right, it has negative growth.

Front

What is a growth triangle in the context of linear relationships?

Back

A growth triangle is a right triangle formed by two points on a graph and the horizontal and vertical lines connecting them. It helps visualize the slope as the rise over run.