Find the Slope from Graphs, Tables and Equations

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 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) can be calculated using the formula: m = (y2 - y1) / (x2 - x1).

Front

What is the slope of a horizontal line?

Back

The slope of a horizontal line is 0.

Front

What is the slope of a vertical line?

Back

The slope of a vertical line is undefined.

Front

If a line rises from left to right, what is the sign of its slope?

Back

The slope is positive.

Front

If a line falls from left to right, what is the sign of its slope?

Back

The slope is negative.

Front

What does a slope of 1 indicate about a line?

Back

A slope of 1 indicates that for every unit increase in x, there is a corresponding unit increase in y, resulting in a 45-degree angle with the x-axis.

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 slope formula: m = (y2 - y1) / (x2 - x1).

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 does the slope affect the graph of a linear equation?

Back

The slope determines the angle and direction of the line on the graph; a steeper slope indicates a steeper line.