Lines y=mx+b

Front

What does the slope (m) represent in the equation y = mx + b?

Back

The slope (m) represents the rate of change of y with respect to x, indicating how steep the line is and the direction it goes (positive or negative).

Front

What is the y-intercept (b) in the equation y = mx + b?

Back

The y-intercept (b) is the point where the line crosses the y-axis, represented as the coordinate (0, b).

Front

How can you determine if a slope is positive, negative, or zero from a graph?

Back

A positive slope rises from left to right, a negative slope falls from left to right, and a zero slope is a horizontal line.

Front

What is an undefined slope, and when does it occur?

Back

An undefined slope occurs when a line is vertical, meaning it does not have a defined rise over run.

Front

How do you find the slope of a line given 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 general form of a linear equation?

Back

The general form of a linear equation is y = mx + b, where m is the slope and b is the y-intercept.

Front

What does it mean for a line to have a negative slope?

Back

A line with a negative slope decreases in value as x increases, indicating an inverse relationship between x and y.

Front

How can you identify the y-intercept from a linear equation?

Back

The y-intercept can be identified as the constant term (b) in the equation y = mx + b.

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 using the slope and y-intercept?

Back

Start at the y-intercept on the y-axis, then use the slope to determine the rise over run to plot additional points.