Slope-Intercept Equations & Comparing Proportional Relationships

Front

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

Back

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

Front

How do you determine if a relationship is proportional?

Back

A relationship is proportional if it can be represented by a straight line that passes through the origin (0,0) on a graph.

Front

What does the slope of a line represent in a real-world context?

Back

The slope represents the rate of change, indicating how much the dependent variable (y) changes for a unit change in the independent variable (x).

Front

How can you compare the rates of two different producers?

Back

You can compare the rates by analyzing the slopes of their production lines on a graph or by comparing their production rates directly.

Front

What is the significance of the y-intercept in a linear equation?

Back

The y-intercept represents the value of y when x is zero, indicating the starting point of the relationship.

Front

How do you write an equation from a given slope and y-intercept?

Back

Use the slope-intercept form y = mx + b, substituting m for the slope and b for the y-intercept.

Front

What is a proportional relationship in terms of a graph?

Back

A proportional relationship is represented by a straight line that passes through the origin, indicating a constant ratio between x and y.

Front

How can you find the price per pound from a table of prices based on weight?

Back

Divide the total price by the weight to find the price per pound.

Front

What is the formula to calculate the slope between two points (x1, y1) and (x2, y2)?

Back

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

Front

What does it mean if one line is steeper than another on a graph?

Back

A steeper line indicates a greater rate of change; thus, the variable represented by that line changes more rapidly than the other.