Interpreting Slope and Y-intercept

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

What does the slope (m) represent 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 (b) represent in a linear equation?

Back

The y-intercept (b) represents the value of y when x is 0, indicating where the line crosses the y-axis.

Front

If m = 2 and b = 5, what is the slope-intercept equation?

Back

y = 2x + 5

Front

In the equation y = 0.5x + 10, what does the y-intercept tell us?

Back

The y-intercept tells us that when x = 0, y = 10.

Front

How do you find the slope from two points (x1, y1) and (x2, y2)?

Back

The slope (m) is calculated as m = (y2 - y1) / (x2 - x1).

Front

What is the meaning of a negative slope in a linear equation?

Back

A negative slope indicates that as x increases, y decreases, showing an inverse relationship.

Front

If a bike rental costs $4 plus $1.50 per hour, how can this be expressed as a linear equation?

Back

The equation is y = 1.5x + 4, where y is the total cost and x is the number of hours.

Front

In the equation c = 0.20t + 3.50, what does the 3.50 represent?

Back

The 3.50 represents the initial cost to rent the kayak before any time is added.

Front

What does the variable x represent in the equation y = 0.25x + 5 for a music service?

Back

The variable x represents the number of songs the customer downloads each month.