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

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 as x changes.

Front

What is an undefined slope?

Back

An undefined slope occurs in a vertical line where x remains constant and y changes.

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

Find the slope of the line that passes through (2, 3) and (4, 7).

Back

m = (7 - 3) / (4 - 2) = 4 / 2 = 2.

Front

What is the slope of the line represented by the equation y = -3x + 5?

Back

The slope is -3.

Front

What is the y-intercept in the equation y = 2x + 4?

Back

The y-intercept is 4.