Real World 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 or negative).

Front

What is the y-intercept of a linear equation?

Back

The y-intercept is the point where the line crosses the y-axis. It is the value of y when x is 0.

Front

How do you find the slope from two points?

Back

The slope (m) can be calculated using the formula m = (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are the coordinates of the two points.

Front

What does it mean if a line has a positive slope?

Back

A line with a positive slope rises from left to right, indicating that as x increases, y also increases.

Front

What does it mean if a line has a negative slope?

Back

A line with a negative slope falls from left to right, indicating that as x increases, y decreases.

Front

What is the formula for calculating the rate of change?

Back

The rate of change can be calculated using the formula: Rate of Change = (Change in y) / (Change in x).

Front

How can you determine the y-intercept from an equation?

Back

To find the y-intercept from an equation in the form y = mx + b, simply identify the value of b.

Front

What is the significance of the x-intercept?

Back

The x-intercept is the point where the line crosses the x-axis. It is the value of x when y is 0.

Front

How do you graph a linear equation?

Back

To graph a linear equation, find the y-intercept, plot it on the graph, use the slope to find another point, and draw a straight line through the points.