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.

Front

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

Back

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

Front

What is a positive slope?

Back

A positive slope means that as x increases, y also increases. The line rises from left to right.

Front

What is a negative slope?

Back

A negative slope means that as x increases, y decreases. The line falls from left to right.

Front

What is zero slope?

Back

A zero slope indicates a horizontal line where y remains constant regardless of x.

Front

What is an undefined slope?

Back

An undefined slope occurs with a vertical line where x remains constant, and the slope cannot be calculated.

Front

If a line has a slope of 1/2, what does this mean?

Back

A slope of 1/2 means that for every 2 units the line moves horizontally to the right, it moves 1 unit vertically up.

Front

What is the slope of the line represented by the equation y = 3x + 2?

Back

The slope of the line is 3.

Front

What is the y-intercept in the equation y = mx + b?

Back

The y-intercept (b) is the point where the line crosses the y-axis.