Find Slope Graphically

Front

What is the slope of a line?

Back

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

Front

How do you find the slope graphically?

Back

To find the slope graphically, select two points on the line, determine the vertical change (rise) and the horizontal change (run) between these points, and then divide the rise by the run (slope = rise/run).

Front

What does a positive slope indicate?

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?

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 vertical change (rise) regardless of the horizontal change (run).

Front

What is the slope of a vertical line?

Back

The slope of a vertical line is undefined, as the run is 0 and division by zero is not possible.

Front

If a line rises 3 units for every 4 units it runs, what is the slope?

Back

The slope is 3/4.

Front

If a line falls 2 units for every 1 unit it runs, what is the slope?

Back

The slope is -2.

Front

What is the slope of the line represented by the points (1, 2) and (3, 6)?

Back

The slope is (6-2)/(3-1) = 4/2 = 2.

Front

How do you interpret a slope of 1?

Back

A slope of 1 means that for every 1 unit increase in x, there is a corresponding 1 unit increase in y, indicating a 45-degree angle line.