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 = 4x?

Back

To graph y = 4x, start at the origin (0,0). From there, use the slope of 4 to rise 4 units up and run 1 unit to the right to find another point (1,4). Connect these points to form a straight line.

Front

What is the graph of y = -x + 3?

Back

The graph of y = -x + 3 is a straight line that crosses the y-axis at (0,3) and has a slope of -1, meaning it goes down 1 unit for every 1 unit it moves to the right.

Front

How do you determine the slope from a linear equation in slope-intercept form?

Back

In the slope-intercept form y = mx + b, the slope (m) is the coefficient of x. For example, in y = 3x - 4, the slope is 3.

Front

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

Back

If a linear equation has a slope of 0, it means the line is horizontal and does not rise or fall as x changes. The equation is of the form y = b.

Front

How can you find the x-intercept of a linear equation?

Back

To find the x-intercept, set y = 0 in the equation and solve for x. The x-intercept is the point where the line crosses the x-axis.

Front

What is the significance of the point (0, b) in a linear equation?

Back

The point (0, b) is the y-intercept of the line, indicating where the line crosses the y-axis.

Front

How do you graph the equation y = 3x - 4?

Back

To graph y = 3x - 4, start at the y-intercept (0, -4). From there, use the slope of 3 to rise 3 units up and run 1 unit to the right to find another point (1, -1). Connect these points.