Graphing 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 (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 (positive slope goes up, negative slope goes down).

Front

What is the y-intercept (b) in a linear equation?

Back

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

Front

How do you graph the equation y = mx + b?

Back

1. Start at the y-intercept (0, b) on the y-axis. 2. Use the slope (m) to find another point: rise/run. 3. Draw a straight line through the points.

Front

What is the graph of y = 2/3x - 1?

Back

The graph is a straight line with a slope of 2/3 and a y-intercept of -1.

Front

How do you determine if a graph represents the equation y = -x + 2?

Back

Check if the line has a slope of -1 (decreasing) and crosses the y-axis at (0, 2).

Front

What is the graph of y = 4x?

Back

The graph is a straight line that passes through the origin (0, 0) with a slope of 4, indicating a steep increase.

Front

How do you graph y = 2/3x - 3?

Back

Start at (0, -3) on the y-axis, then use the slope of 2/3 to find another point, and draw the line.

Front

What does the equation y = x - 4 represent?

Back

It represents a straight line with a slope of 1 and a y-intercept of -4.

Front

What is the significance of the slope being zero?

Back

A slope of zero indicates a horizontal line, meaning y does not change as x changes.