Comparing Linear Functions

Front

What does the y-intercept of a linear function represent?

Back

The y-intercept represents the value of y when x is 0, often interpreted as the initial value or fixed cost in real-world scenarios.

Front

In the equation y = mx + b, what does 'm' represent?

Back

'm' represents the slope of the line, indicating the rate of change of y with respect to x.

Front

In the equation y = mx + b, what does 'b' represent?

Back

'b' represents the y-intercept, the point where the line crosses the y-axis.

Front

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

Back

Slope (m) = (y2 - y1) / (x2 - x1).

Front

What is the slope of the line represented by the equation y = 4x + 2?

Back

The slope is 4.

Front

If a gym charges a monthly fee plus a per-visit fee, how can this be represented mathematically?

Back

This can be represented as y = mx + b, where m is the per-visit fee and b is the monthly fee.

Front

What is the significance of the slope in a real-world context?

Back

The slope indicates how much the dependent variable (y) changes for each unit increase in the independent variable (x).

Front

If two linear equations have the same slope, what can be said about their graphs?

Back

If two linear equations have the same slope, their graphs are parallel and will never intersect.

Front

How can you determine which of two linear functions is greater at a specific x-value?

Back

Substitute the x-value into both equations and compare the resulting y-values.

Front

What does it mean if two linear equations intersect at a point?

Back

It means that the two equations have the same value for both x and y at that point, indicating a solution to the system of equations.