Linear Equations Flashcard 1

Front

What is the slope of a line?

Back

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

Front

How do you find 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 is the y-intercept of a line?

Back

The y-intercept is the point where the line crosses the y-axis, represented as 'b' in the slope-intercept form of a line, y = mx + b.

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 do you determine the y-intercept from a linear equation?

Back

To find the y-intercept, set x = 0 in the equation and solve for y.

Front

What does a positive slope indicate about a line?

Back

A positive slope indicates that as x increases, y also increases, 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 x increases, y decreases, meaning the line falls from left to right.

Front

How can you identify the slope from a graph?

Back

The slope can be identified by selecting two points on the line, calculating the rise (change in y) and run (change in x), and then using the formula m = rise/run.

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.

Front

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

Back

Start by plotting the y-intercept (b) on the y-axis, then use the slope (m) to determine the rise/run to plot a second point.