8.5I All Representations Review

Front

What is the slope-intercept form of a linear equation?

Back

The slope-intercept form of a linear equation is given by y = mx + b, where m is the slope and b is the y-intercept.

Front

How do you identify the slope from the equation y = mx + b?

Back

The slope (m) is the coefficient of x in the equation y = mx + b.

Front

What does the y-intercept represent in a linear equation?

Back

The y-intercept (b) represents the point where the line crosses the y-axis, indicating the value of y when x = 0.

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 in terms of x.

Front

What is the significance of the slope in a linear equation?

Back

The slope indicates the rate of change of y with respect to x; it shows how much y increases or decreases as x increases by one unit.

Front

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

Back

The slope (m) between two points is calculated using the formula m = (y2 - y1) / (x2 - x1).

Front

What is the meaning of a positive slope in a linear graph?

Back

A positive slope indicates that as x increases, y also increases, resulting in an upward slant of the line.

Front

What does a negative slope indicate about the relationship between x and y?

Back

A negative slope indicates that as x increases, y decreases, resulting in a downward slant of the line.

Front

How do you write an equation for a real-world scenario involving costs?

Back

To write an equation for a real-world scenario, identify the fixed costs and variable costs, then express the total cost as y = mx + b.

Front

What is the formula for calculating total cost when there is a fixed charge and a variable charge per unit?

Back

The total cost can be calculated using the formula y = mx + b, where m is the variable cost per unit, and b is the fixed charge.