Slope & Graphing Linear Equations Academic 2024-2025

Front

What is the definition of slope in a linear equation?

Back

The slope of a line is a measure of its steepness, typically represented as 'm' in the equation of a line, defined as the ratio of the rise (change in y) over the run (change in x).

Front

How do you calculate the slope between 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-value increases, the y-value also increases, resulting in an upward slant from left to right.

Front

What does a negative slope indicate about a line?

Back

A negative slope indicates that as the x-value increases, the y-value decreases, resulting in a downward slant 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-value changes.

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

How do you graph a linear equation in slope-intercept form?

Back

To graph a linear equation in the form y = mx + b, start at the y-intercept (b) on the y-axis, then use the slope (m) to find another point.

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

What does the term 'y-intercept' refer to?

Back

The y-intercept is the point where the line crosses the y-axis, represented by the value of b in the slope-intercept form.

Front

What is the significance of the slope in real-world applications?

Back

The slope can represent rates of change, such as speed, cost per item, or growth rates in various contexts.