Writing Equations from Tables

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 (m) represent in a linear equation?

Back

The slope (m) represents the rate of change of y with respect to x. It indicates how steep the line is and the direction it goes.

Front

What does the y-intercept (b) 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 determine the equation of a line from a table of values?

Back

To determine the equation, find the slope (m) by calculating the change in y over the change in x, and then use a point from the table to find the y-intercept (b).

Front

What is the equation for a line with a slope of 4 and a y-intercept of 3?

Back

The equation is y = 4x + 3.

Front

If a table shows that when x = 1, y = 6, and when x = 2, y = 8, what is the slope?

Back

The slope is 2, calculated as (8 - 6) / (2 - 1).

Front

What is the equation for a line that passes through the points (0, 5) and (1, 6)?

Back

The equation is y = x + 5.

Front

How can you tell if an equation is linear?

Back

An equation is linear if it can be written in the form y = mx + b, where m and b are constants.

Front

What does it mean if the slope of a line is negative?

Back

A negative slope means that as x increases, y decreases, indicating a downward trend in the graph.

Front

What is the equation for a line with a slope of 0?

Back

The equation is y = b, where b is a constant. This represents a horizontal line.