Slope

Front

What is the definition of slope in a linear equation?

Back

The slope of a line is a measure of its steepness, typically represented as 'm' in the equation of a line (y = mx + b). It is calculated as the change in y divided by the change in x (rise/run).

Front

How do you find the y-intercept of a linear equation?

Back

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

Front

What is the formula to calculate 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 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 horizontal line?

Back

The slope of a horizontal line is 0, as there is no change in y regardless of the change in x.

Front

What is the slope of a vertical line?

Back

The slope of a vertical line is undefined, as the change in x is 0, leading to division by zero in the slope formula.

Front

How can 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 use the slope formula (rise/run).

Front

What is the significance of the slope in real-world applications?

Back

The slope can represent rates of change in real-world contexts, such as speed, growth rates, or any situation where one quantity changes in relation to another.

Front

How do you interpret a slope of 1/2 in a real-world context?

Back

A slope of 1/2 means that for every 1 unit increase in x, y increases by 0.5 units, indicating a gradual increase.