FOM: CW 4.3 Finding Slope from a Graph

Front

What is the definition of slope in a graph?

Back

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

Front

How do you calculate the slope from a graph?

Back

To calculate the slope from a graph, select two points on the line, determine the rise (change in y) and run (change in x), and use the formula: Slope (m) = rise/run.

Front

What does a positive slope indicate about a line?

Back

A positive slope indicates that as the x-values increase, the y-values also increase, 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-values increase, the y-values decrease, 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, indicating no vertical change as the x-values change.

Front

What is the slope of a vertical line?

Back

The slope of a vertical line is undefined because the run (change in x) is 0, leading to division by zero.

Front

If a line rises 4 units and runs 2 units, what is the slope?

Back

The slope is 2, calculated as Slope (m) = rise/run = 4/2 = 2.

Front

If a line falls 3 units and runs 6 units, what is the slope?

Back

The slope is -0.5, calculated as Slope (m) = rise/run = -3/6 = -0.5.

Front

What is the slope of the line represented by the equation y = 2x + 3?

Back

The slope of the line is 2, which is the coefficient of x in the equation.

Front

What is the slope of the line represented by the equation y = -rac{1}{4}x + 5?

Back

The slope of the line is -rac{1}{4}, indicating a negative slope.