Finding Slope From a Graph and Table

Front

What is the definition of slope in a graph?

Back

The slope of a graph 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

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-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 change in x (run) is 0, leading to division by zero.

Front

If a line has a slope of 2, what does this mean?

Back

A slope of 2 means that for every 1 unit increase in x, the y-value increases by 2 units.

Front

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

Back

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

Front

What is the slope of the line represented by the equation y = 3x + 1?

Back

The slope of the line is 3, which indicates that for every 1 unit increase in x, y increases by 3 units.

Front

What is the slope of the line represented by the equation y = -1/2x + 4?

Back

The slope of the line is -1/2, indicating that for every 1 unit increase in x, y decreases by 0.5 units.