Linear Equations & Graphs

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 (upward or downward).

Front

What is the y-intercept in a linear equation?

Back

The y-intercept is the point where the line crosses the y-axis. It is represented by the value of b in the slope-intercept form y = mx + b.

Front

How do you convert an equation to slope-intercept form?

Back

To convert an equation to slope-intercept form (y = mx + b), solve for y in terms of x.

Front

What is the slope-intercept form of the equation 2y = 10x + 14?

Back

The slope-intercept form is y = 5x + 7.

Front

What does a positive slope indicate about a line?

Back

A positive slope indicates that as x increases, y also increases, meaning the line rises from left to right.

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 can you identify the slope from a graph?

Back

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

Front

What is the standard form of a linear equation?

Back

The standard form of a linear equation is Ax + By = C, where A, B, and C are integers, and A should be non-negative.

Front

What is the significance of the x-intercept?

Back

The x-intercept is the point where the line crosses the x-axis, indicating the value of x when y is zero.