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. 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 in a linear relationship?

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 in a linear equation?

Back

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

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). In this case, the equation can be written as y = kx, where k is a constant.

Front

How can you identify a proportional relationship from a graph?

Back

A proportional relationship can be identified from a graph if the line passes through the origin (0,0) and has a constant slope.

Front

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

Back

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

Front

How do you find the slope from two points on a line?

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 does it mean if a line has a positive slope?

Back

If a line has a positive slope, it means that as the x-value increases, the y-value also increases. This indicates a direct relationship between the two variables.

Front

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

Back

If a line has a negative slope, it means that as the x-value increases, the y-value decreases. This indicates an inverse relationship between the two variables.

Front

What is the difference between a linear equation and a nonlinear equation?

Back

A linear equation represents a straight line when graphed, while a nonlinear equation represents a curve. Linear equations have a constant rate of change, whereas nonlinear equations do not.