Graphing 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

How do you determine if a slope is positive or negative from a graph?

Back

A slope is positive if the line rises from left to right and negative if it falls from left to right.

Front

What is the y-intercept of a line?

Back

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

Front

How can you find the slope from two points on a line?

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 is the Slope-Intercept Form of a linear equation?

Back

The Slope-Intercept Form of a linear equation is y = mx + b, where m is the slope and b is the y-intercept.

Front

What does a negative slope indicate about a line?

Back

A negative slope indicates that as x increases, y decreases, meaning the line falls from left to right.

Front

How do you graph a linear equation in slope-intercept form?

Back

To graph a linear equation in slope-intercept form, start at the y-intercept (b) on the y-axis, then use the slope (m) to determine the rise over run to find another point.

Front

What is the significance of the slope in real-world applications?

Back

In real-world applications, the slope can represent rates such as speed, cost per item, or any other rate of change.

Front

How can you convert a linear equation from standard form to slope-intercept form?

Back

To convert from standard form (Ax + By = C) to slope-intercept form (y = mx + b), solve for y to isolate it on one side of the equation.