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 of a line represent?

Back

The slope of a line 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 in a linear equation?

Back

The y-intercept is the point where the line crosses the y-axis. It is represented by the value of b in the equation y = mx + b.

Front

How do you identify the slope from the equation y = -¼x + 3?

Back

The slope is -¼, indicating that for every 4 units you move to the right on the x-axis, the line moves down 1 unit.

Front

What does a negative slope indicate about a line?

Back

A negative slope indicates that as x increases, y decreases, meaning the line goes downwards from left to right.

Front

How can you determine the graph of y = -x + 3?

Back

To graph y = -x + 3, start at the y-intercept (0, 3) and use the slope of -1 to find another point (1, 2). Connect these points to form the line.

Front

What is the significance of the equation y = -2x + 4?

Back

In this equation, the slope is -2, meaning the line is steep and decreases quickly. The y-intercept is 4, where the line crosses the y-axis.

Front

How do you find the graph of y = ⅔x - 1?

Back

Start at the y-intercept (0, -1) and use the slope of ⅔ to find another point (3, 0). Connect these points to graph the line.

Front

What does the term 'graphing' mean in mathematics?

Back

Graphing is the process of plotting points on a coordinate plane to represent equations or functions visually.

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.