Linear Equations

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 linear equation represent?

Back

The slope 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 is the y-intercept in a linear equation?

Back

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

Front

How do you find the rate of change from a linear equation?

Back

The rate of change can be found by calculating the slope (m) of the line, which is the change in y divided by the change in x.

Front

What is the initial value in the context of linear equations?

Back

The initial value is the y-intercept of the linear equation, representing the starting value of y when x is 0.

Front

If a linear equation has a slope of -2, what does this indicate?

Back

A slope of -2 indicates that for every 1 unit increase in x, y decreases by 2 units.

Front

What does it mean if the slope of a linear equation is 0?

Back

If the slope is 0, it means the line is horizontal, indicating that there is no change in y as x changes.

Front

How can you determine the slope from a graph?

Back

To determine the slope from a graph, select two points on the line, calculate the rise (change in y) and run (change in x), and divide rise by run.

Front

What is the formula for calculating the slope between two points (x1, y1) and (x2, y2)?

Back

The formula for slope (m) is m = (y2 - y1) / (x2 - x1).

Front

What does it mean if a linear equation has an undefined slope?

Back

An undefined slope occurs when the line is vertical, meaning x does not change regardless of the value of y.