FInding Slope

Front

What is the definition of slope in mathematics?

Back

Slope is a measure of the steepness or incline of a line, typically represented as 'm' in the slope-intercept form of a linear equation (y = mx + b). It is calculated as the change in y divided by the change in x (rise/run).

Front

How do you calculate the slope between two points (x1, y1) and (x2, y2)?

Back

The slope (m) is 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 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.

Front

If a line has a slope of -3, what does this mean in terms of rise and run?

Back

A slope of -3 means that for every 1 unit you move to the right (run), the line falls 3 units (rise).

Front

What is the slope-intercept form of a linear equation?

Back

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

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 formula m = rise/run.

Front

What is the significance of the y-intercept in the slope-intercept form?

Back

The y-intercept (b) is the point where the line crosses the y-axis, indicating the value of y when x = 0.