Linear Equations and Functions

Front

What is a linear equation?

Back

An equation that makes a straight line when graphed, typically 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 represents the rate of change of y with respect to x, indicating how steep the line is.

Front

How do you find the slope between two points (x1, y1) and (x2, y2)?

Back

Slope (m) = (y2 - y1) / (x2 - x1).

Front

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

Back

The y-intercept (b) is the point where the line crosses the y-axis.

Front

What is the standard form of a linear equation?

Back

Ax + By = C, where A, B, and C are integers.

Front

How can you determine if a function is linear?

Back

A function is linear if it can be expressed in the form y = mx + b and its graph is a straight line.

Front

What is the difference between linear and nonlinear functions?

Back

Linear functions have a constant rate of change and graph as straight lines, while nonlinear functions do not have a constant rate of change and can curve.

Front

What is the equation of a line with slope m = 3 that passes through the point (2, 1)?

Back

y = 3x - 5.

Front

How do you write the equation of a line given two points?

Back

1. Find the slope using the two points. 2. Use the point-slope form: y - y1 = m(x - x1).

Front

What does it mean for a graph to be linear?

Back

A linear graph is a straight line, indicating a constant relationship between the variables.