Slope All Ways

Front

What is the definition of slope in a linear equation?

Back

The slope is a measure of the steepness or incline of a line, represented as the ratio of the vertical change (rise) to the horizontal change (run) between two points on the line.

Front

How do you find the slope from an equation in slope-intercept form?

Back

In the slope-intercept form of a linear equation, y = mx + b, the slope (m) is the coefficient of x.

Front

What are the x- and y-intercepts of a linear equation?

Back

The x-intercept is the point where the line crosses the x-axis (y=0), and the y-intercept is the point where the line crosses the y-axis (x=0).

Front

How do you calculate the slope from 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 the x-value increases, the y-value 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 the x-value increases, the y-value decreases, meaning the line falls from left to right.

Front

What does an undefined slope indicate?

Back

An undefined slope indicates a vertical line, where the x-value does not change, resulting in a division by zero when calculating slope.

Front

What is the slope of a horizontal line?

Back

The slope of a horizontal line is 0, indicating that there is no vertical change as the x-value changes.

Front

How can you determine the slope from a table of values?

Back

To determine the slope from a table, select two points (x1, y1) and (x2, y2) from the table and use the slope formula m = (y2 - y1) / (x2 - x1).

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, cost per item, or growth rates.