CC3 (Ch. 4) 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 a linear equation of the form y = mx + b.

Front

What does the 'm' represent in the equation y = mx + b?

Back

The 'm' represents the slope of the line, which indicates the rate of change of y with respect to x.

Front

What does the 'b' represent in the equation y = mx + b?

Back

The 'b' represents the y-intercept, which 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 is the constant rate of change in a linear relationship?

Back

The constant rate of change is the same as the slope of the line, indicating how much y changes for a unit change in x.

Front

If the slope of a line is positive, what does that indicate about the relationship between x and y?

Back

A positive slope indicates that as x increases, y also increases.

Front

If the slope of a line is negative, what does that indicate about the relationship between x and y?

Back

A negative slope indicates that as x increases, y decreases.

Front

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

Back

The equation is y = 3x + 2.

Front

How can you determine if a point (x, y) lies on a line represented by the equation y = mx + b?

Back

Substitute the x-value into the equation to see if the resulting y-value matches the y-value of the point.

Front

What is the significance of the y-intercept in a real-world context?

Back

The y-intercept can represent the starting value of a situation before any changes occur.