Linear Equations and Slope

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 the slope of a vertical line?

Back

The slope of a vertical line is undefined.

Front

What is the slope of a horizontal line?

Back

The slope of a horizontal line is 0.

Front

What does it mean if the slope is positive?

Back

A positive slope means that as x increases, y also increases, indicating an upward trend.

Front

What does it mean if the slope is negative?

Back

A negative slope means that as x increases, y decreases, indicating a downward trend.

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, represented by the value of y when x = 0.

Front

How can you identify the slope from a graph?

Back

The slope can be identified by selecting two points on the line and using the rise over run method: rise (change in y) over run (change in x).

Front

What is the equation of a line with a slope of 4 and a y-intercept of 2?

Back

The equation is y = 4x + 2.