8th Linear Relationships

Front

What is a linear relationship?

Back

A linear relationship is a relationship between two variables that can be represented by a straight line on a graph. It can be described by the equation y = mx + b, where m is the slope and b is the y-intercept.

Front

What is the slope in a linear equation?

Back

The slope (m) of a linear equation represents the rate of change of the dependent variable (y) with respect to the independent variable (x). It indicates how steep the line is.

Front

What does the y-intercept represent in a linear equation?

Back

The y-intercept (b) is the point where the line crosses the y-axis. It represents the value of y when x is 0.

Front

How do you find 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 formula for a linear equation in slope-intercept form?

Back

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

Front

What does a positive slope indicate about a linear relationship?

Back

A positive slope indicates that as the independent variable (x) increases, the dependent variable (y) also increases.

Front

What does a negative slope indicate about a linear relationship?

Back

A negative slope indicates that as the independent variable (x) increases, the dependent variable (y) decreases.

Front

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

Back

The y-intercept can be determined by setting x = 0 in the equation and solving for y.

Front

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

Back

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

Front

How do you graph a linear equation?

Back

To graph a linear equation, identify the y-intercept, plot it on the graph, and use the slope to find another point. Draw a straight line through the points.