Linear Relationships Retake

Front

What is a linear relationship?

Back

A linear relationship is a relationship between two variables that can be represented by a straight line on a graph, typically expressed in the form of an equation 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 of a linear equation represents the rate of change of the dependent variable (y) with respect to the independent variable (x). It indicates how much y changes for a one-unit increase in x.

Front

What is the y-intercept in a linear equation?

Back

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

Front

How do you determine if a table of values represents a linear relationship?

Back

A table of values represents a linear relationship if the differences between consecutive y-values divided by the differences between consecutive x-values are constant.

Front

What is the equation of a line in slope-intercept form?

Back

The equation of a line in slope-intercept form is written as y = mx + b, where m is the slope and b is the y-intercept.

Front

How can you find the total cost of a project given a fixed fee and a variable cost per hour?

Back

The total cost can be calculated using the formula: Total Cost = Fixed Fee + (Variable Cost per Hour * Number of Hours).

Front

What is the significance of the equation y = 0.5x + 14?

Back

This equation represents a linear relationship where the slope is 0.5, indicating that for every 1 unit increase in x, y increases by 0.5 units, and the y-intercept is 14.

Front

How do 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 by isolating it on one side of the equation.

Front

What does the term 'membership fee' imply in a linear cost model?

Back

A membership fee is a fixed cost that must be paid upfront, which does not change regardless of usage, while additional costs may vary based on usage.

Front

How do you interpret the graph of a linear equation?

Back

The graph of a linear equation shows the relationship between the two variables, with the slope indicating the direction and steepness of the line, and the y-intercept indicating where the line crosses the y-axis.