Linear Equations and Cost Models

Front

What is a linear equation?

Back

A linear equation is an equation that makes a straight line when graphed. It can be written in the form y = mx + b, where m is the slope and b is the y-intercept.

Front

What does the slope of a line represent?

Back

The slope of a line represents the rate of change of y with respect to x. It indicates how much y changes for a unit change in x.

Front

What is the y-intercept in a linear equation?

Back

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

Front

How do you find the slope from two points?

Back

The slope (m) can be calculated using the formula m = (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are the two points.

Front

What is slope-intercept form?

Back

Slope-intercept form is a way of writing linear equations as y = mx + b, where m is the slope and b is the y-intercept.

Front

What does a positive slope indicate?

Back

A positive slope indicates that as x increases, y also increases, showing a direct relationship between the two variables.

Front

What does a negative slope indicate?

Back

A negative slope indicates that as x increases, y decreases, showing an inverse relationship between the two variables.

Front

What is the rate of change in a linear relationship?

Back

The rate of change is the same as the slope of the line and represents how much one quantity changes in relation to another.

Front

How can you write an equation from a graph?

Back

To write an equation from a graph, identify the slope and y-intercept, then use the slope-intercept form y = mx + b.

Front

What is the equation of a line with a slope of 2 and a y-intercept of 3?

Back

The equation is y = 2x + 3.