Flashcard Review-Slope and Equation of a Line

Front

What is the slope of a line?

Back

The slope of a line is a measure of its steepness, usually represented as 'm' in the equation of a line. It is calculated as the change in y divided by the change in x (rise over run).

Front

How do you find the y-intercept of a line?

Back

The y-intercept is the point where the line crosses the y-axis. It can be found by setting x to 0 in the equation of the line.

Front

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

Back

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

Front

Calculate the slope between the points (2, 3) and (4, 7).

Back

The slope (m) is calculated as (7 - 3) / (4 - 2) = 4 / 2 = 2.

Front

What does a positive slope indicate about a line?

Back

A positive slope indicates that as x increases, y also increases, meaning the line rises from left to right.

Front

What does a negative slope indicate about a line?

Back

A negative slope indicates that as x increases, y decreases, meaning the line falls from left to right.

Front

What is the slope of a vertical line?

Back

The slope of a vertical line is undefined because the change in x is zero, leading to division by zero.

Front

What is the slope of a horizontal line?

Back

The slope of a horizontal line is 0 because there is no change in y as x changes.

Front

If a line has a slope of 3, what does this mean?

Back

A slope of 3 means that for every 1 unit increase in x, y increases by 3 units.

Front

How do you determine the slope from a graph?

Back

To determine the slope from a graph, select two points on the line, calculate the rise (change in y) and run (change in x), and then divide rise by run.