Algebra Camp: 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 or negative).

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 = ⅖x + 2?

Back

To graph y = ⅖x + 2, start at the y-intercept (0, 2). From there, use the slope ⅖ to rise 2 units and run 5 units to the right to find another point.

Front

What is the graph of y = x - 2?

Back

The graph of y = x - 2 is a straight line that crosses the y-axis at (0, -2) and has a slope of 1.

Front

How do you find the y-intercept of the equation y = 3x - 4?

Back

To find the y-intercept of y = 3x - 4, set x = 0. This gives y = -4, so the y-intercept is (0, -4).

Front

What does it mean if a line has a negative slope?

Back

A line with a negative slope means that as x increases, y decreases. The line goes down from left to right.

Front

How do you graph a horizontal line like y = -3?

Back

To graph y = -3, draw a horizontal line that crosses the y-axis at -3. This line has a slope of 0.

Front

What is the difference between a positive slope and a negative slope?

Back

A positive slope means the line rises from left to right, while a negative slope means the line falls from left to right.

Front

What is the standard form of a linear equation?

Back

The standard form of a linear equation is Ax + By = C, where A, B, and C are integers, and A should be non-negative.