Slope-Intercept Equations & Comparing Proportional Relationships

Front

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

Back

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

Front

How do you identify a proportional relationship from a graph?

Back

A proportional relationship can be identified from a graph if the line passes through the origin (0,0) and has a constant slope.

Front

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

Back

The slope of a line represents the rate of change between the two variables, indicating how much one variable changes for a unit change in the other variable.

Front

How can you determine which of two companies offers a better price per unit?

Back

To determine which company offers a better price per unit, calculate the price per unit for each company and compare the values; the lower price per unit is the better deal.

Front

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

Back

The y-intercept is the point where the line crosses the y-axis, representing the value of y when x is zero.

Front

How do you compare the rates of production between two companies using their graphs?

Back

To compare the rates of production, look at the slopes of the lines on the graph; a steeper slope indicates a higher rate of production.

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.

Front

What does it mean for a relationship to be proportional?

Back

A relationship is proportional if it can be expressed as a constant ratio between two quantities, meaning that as one quantity increases, the other increases at a constant rate.

Front

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

Back

To write an equation from a given slope (m) and y-intercept (b), use the slope-intercept form: y = mx + b.

Front

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

Back

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