Graphing Linear Equations

Front

What is the definition of 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 the equation y = mx + b?

Back

The y-intercept is the value of y when x is 0. It is represented by the variable b in the equation.

Front

How do you find the slope from two points (x1, y1) and (x2, y2)?

Back

The slope (m) can be calculated using the formula m = (y2 - y1) / (x2 - x1).

Front

What does a positive slope indicate about a line?

Back

A positive slope indicates that as x increases, y also increases, meaning the line rises from left to right.

Front

What does a negative slope indicate about a line?

Back

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

Front

What is the slope of the line represented by the equation y = 5x + 1?

Back

The slope of the line is 5.

Front

What is the slope of a horizontal line?

Back

The slope of a horizontal line is 0.

Front

What is the slope of a vertical line?

Back

The slope of a vertical line is undefined.

Front

How can you determine if a line is increasing or decreasing from its equation?

Back

If the slope (m) is positive, the line is increasing. If the slope is negative, the line is decreasing.