Write Slope-Intercept Form for Word Problems

Front

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

Back

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

Front

How do you identify the slope in a linear equation?

Back

The slope (m) represents the rate of change of y with respect to x, indicating how much y changes for a unit change in x.

Front

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

Back

The y-intercept (b) is the value of y when x is 0, representing the starting point of the line on the y-axis.

Front

How can you convert a word problem into slope-intercept form?

Back

Identify the initial value (y-intercept) and the rate of change (slope) from the problem, then express it as y = mx + b.

Front

In the problem, 'The population of Florida would be about 17.4 million in 2010 and increase by 0.22 million per year,' what is the slope?

Back

The slope is 0.22, representing the annual increase in population.

Front

In the bike rental problem, what does the $4 represent?

Back

The $4 represents the fixed cost or y-intercept, which is the base fee for renting the bike.

Front

What is the total income equation for selling x calendars at $5 each?

Back

The equation is y = 5x, where y is the total income and x is the number of calendars sold.

Front

If Cameron sells 200 calendars, how do you calculate the total income?

Back

Use the equation y = 5x. Substitute x with 200: y = 5(200) = $1000.

Front

What is the significance of the rate of descent in the airplane problem?

Back

The rate of descent (2,000 feet per minute) is the slope, indicating how quickly the altitude decreases.

Front

How do you find the altitude of the plane after 5 minutes?

Back

Start at 30,000 feet and subtract the total descent: 30,000 - (2,000 * 5) = 20,000 feet.