Question

Use the graph below to answer the following equations.

1,5 7.2,20

Part A) Write the function of the line in function notation.

Part B) What is the rate of change of the line? What does the rate of change represent in this situation?

Part C) What is the y-intercept of the line? What does the y-intercept represent in this situation?

Answer 1

[AI-generated answer — Bot GPT 3.5]

Part A) The function of the line in function notation is y = mx + b, where m is the slope and b is the y-intercept.

Part B) The rate of change of the line is given by the slope, which can be calculated using the two coordinates (1,5) and (7.2,20). The slope (m) is equal to (change in y)/(change in x), which in this case is (20-5)/(7.2-1) = 15/6.2 = 2.419.

The rate of change represents how much the y-coordinate (vertical) changes for every unit increase in the x-coordinate (horizontal). In this situation, for every unit increase in x, the y-coordinate changes by 2.419 units.

Part C) The y-intercept of the line is where the line intersects the y-axis, which is the point (0, b) in the equation y = mx + b. Looking at the graph, it appears that the y-intercept is approximately equal to 2.

The y-intercept represents the value of y when x is zero. In this situation, it could represent a starting value or a baseline measurement.