Key Features of 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, negative, zero, or undefined).

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 a 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 in a vertical line where x remains constant, and y can take any value.

Front

How do you find the x-intercept of a linear equation?

Back

To find the x-intercept, set y = 0 in the equation and solve for x.

Front

How do you find the y-intercept of a linear equation?

Back

To find the y-intercept, set x = 0 in the equation and solve for y.

Front

What is the x-intercept of the equation y = 2x - 2?

Back

The x-intercept is (1, 0). Set y = 0: 0 = 2x - 2, so x = 1.

Front

What is the y-intercept of the equation y = 2x - 2?

Back

The y-intercept is (0, -2). Set x = 0: y = 2(0) - 2, so y = -2.