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?

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 slope-intercept form of a linear equation?

Back

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

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 y-intercept of a line?

Back

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

Front

What does a positive slope indicate?

Back

A positive slope indicates that as the value of x increases, the value of y also increases, resulting in an upward slant of the line.

Front

What does a negative slope indicate?

Back

A negative slope indicates that as the value of x increases, the value of y decreases, resulting in a downward slant of the line.

Front

What is the rate of change in a linear relationship?

Back

The rate of change in a linear relationship is the same as the slope of the line. It measures how much y changes for a unit change in x.

Front

How can you identify the slope from a graph?

Back

To identify the slope from a graph, select two points on the line, determine the rise (change in y) and run (change in x), and then calculate the slope using the formula m = rise/run.

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.