compare linear function

Front

What is a linear function?

Back

A linear function is a function that can be graphically represented as a straight line. It has the form f(x) = mx + b, where m is the slope and b is the y-intercept.

Front

What does the slope of a linear function represent?

Back

The slope of a linear function represents the rate of change of the function. It indicates how much the y-value changes for a unit change in the x-value.

Front

How do you determine the slope from two points on a line?

Back

The slope (m) can be calculated using the formula m = (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are two points on the line.

Front

What is the y-intercept of a linear function?

Back

The y-intercept is the point where the line crosses the y-axis. It is represented by the value of b in the linear function equation f(x) = mx + b.

Front

How can you compare the slopes of two linear functions?

Back

To compare the slopes of two linear functions, examine the coefficients of x in their equations. The function with the larger coefficient has a steeper slope.

Front

What does it mean if one linear function has a greater slope than another?

Back

If one linear function has a greater slope than another, it means that it increases or decreases at a faster rate compared to the other function.

Front

How do you find the y-intercept from a linear equation?

Back

To find the y-intercept from a linear equation in the form y = mx + b, simply identify the value of b, which is the y-coordinate when x = 0.

Front

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

Back

In real-world applications, the y-intercept often represents the initial value or starting point of a situation before any changes occur.

Front

How can you graph a linear function?

Back

To graph a linear function, plot the y-intercept on the y-axis, use the slope to find another point, and draw a straight line through the points.

Front

What happens to the graph of a linear function if the slope is negative?

Back

If the slope of a linear function is negative, the graph will slope downwards from left to right, indicating a decrease in the y-value as the x-value increases.