Slope from Graphs

Front

What is the definition of slope in a graph?

Back

Slope is a measure of the steepness or incline of a line, 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 two points (x1, y1) and (x2, y2)?

Back

Slope (m) = (y2 - y1) / (x2 - x1)

Front

What does a positive slope indicate about a line on a graph?

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 on a graph?

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 regardless of the horizontal change.

Front

What is the slope of a vertical line?

Back

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

Front

If a line has a slope of 3/4, what does this mean in terms of rise and run?

Back

For every 4 units moved horizontally (run), the line rises 3 units vertically (rise).

Front

How can you determine the slope from a graph visually?

Back

To determine the slope visually, select two points on the line, count the vertical change (rise) and the horizontal change (run), and then calculate the slope as rise/run.

Front

What is the slope of the line represented by the equation y = 2x + 1?

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 = -1/2x + 3?

Back

The slope of the line is -1/2, indicating a downward slope.