Writing Linear Equations: Review

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 linear equation represent?

Back

The slope represents the rate of change of the dependent variable (y) with respect to the independent variable (x). It indicates how steep the line is.

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 the value of y when x is 0.

Front

How do you find the slope from two points (x1, y1) and (x2, y2)?

Back

The slope (m) can be calculated using the formula m = (y2 - y1) / (x2 - x1).

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

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

Back

To convert from y = mx + b to Ax + By = C, rearrange the equation to get all terms on one side.

Front

What does the term 'per-mile fee' mean in a linear equation context?

Back

The per-mile fee is the variable cost associated with each mile driven, represented by the slope in the equation.

Front

If y = 2x + 3, what is the slope?

Back

The slope is 2.

Front

If a linear equation has a slope of -1, what does this indicate about the graph?

Back

A slope of -1 indicates that for every unit increase in x, y decreases by 1 unit, resulting in a downward sloping line.

Front

What is the significance of the constant term in a linear equation?

Back

The constant term (b in y = mx + b) represents the y-intercept, indicating the starting value of y when x is 0.