Linear Relationships Multiple Representations

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. It can be expressed in the form of an equation, typically y = mx + b, where m is the slope and b is the y-intercept.

Front

What does the slope of a line represent in a linear equation?

Back

The slope of a line represents the rate of change between the two variables. It indicates how much y changes for a unit change in x.

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 represents the value of y when x is 0.

Front

How do you identify a linear equation from a graph?

Back

A linear equation can be identified from a graph if the points form a straight line. The equation can be derived from the slope and y-intercept.

Front

What is the equation of a line with a slope of 2 and a y-intercept of 3?

Back

The equation is y = 2x + 3.

Front

If a line has a slope of -1, what does this indicate about the relationship between x and y?

Back

A slope of -1 indicates that as x increases, y decreases at the same rate.

Front

What does it mean if two lines are parallel?

Back

Two lines are parallel if they have the same slope but different y-intercepts. They will never intersect.

Front

What does it mean if two lines are perpendicular?

Back

Two lines are perpendicular if the product of their slopes is -1. This means one line has a slope that is the negative reciprocal of the other.

Front

How can you write an equation from a word problem involving a linear relationship?

Back

Identify the variables, determine the fixed costs (y-intercept), and the variable costs (slope) from the problem, then formulate the equation.

Front

What is the formula to calculate the total cost in a linear relationship?

Back

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