810 Acc. Interpreting Slope & Y-intercept

Front

What is the slope in the equation y = mx + b?

Back

The slope (m) represents the rate of change of y with respect to x, indicating how much y increases or decreases as x increases.

Front

What does the y-intercept represent in the equation y = mx + b?

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

Write the equation in slope-intercept form for a bike rental that costs $4 plus $1.50 per hour.

Back

y = 1.50x + 4

Front

What does the slope of the equation y = 0.5x + 10 represent in the context of renting a moving truck?

Back

The slope (0.5) represents the per-mile fee for the moving truck.

Front

If a candle burns out completely in 10 hours, what does this imply about its burn rate?

Back

It implies that the candle has a consistent burn rate that leads to it being fully consumed in 10 hours.

Front

In the equation y = 0.20x + 3.50, what does the y-intercept (3.50) indicate?

Back

It indicates that you have to pay $3.50 up front before using the kayak.

Front

How do you determine the slope from a linear equation?

Back

The slope is the coefficient of x in the equation y = mx + b.

Front

What is the significance of the y-intercept in real-world applications?

Back

The y-intercept often represents a fixed cost or starting value before any variable costs are added.

Front

If the slope of a line is negative, what does that indicate about the relationship between x and y?

Back

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

Front

What is the formula for converting a linear equation into slope-intercept form?

Back

To convert to slope-intercept form, isolate y on one side of the equation: y = mx + b.