Question

Part 1 out of 2Use the graph to make a linear model of each function. Describe the meaning of the termsin the models. Then create the linear system, and state what the solution represents.1000900800200(8,690)600500Apples picked400(0,450)300(0,210)g(1)023Time (h)The y-intercept, b, of f(t) isand the slope, m, of f(t) isSo f(t) =t +The y-intercept, b, of g(t) isand the slope, m, of g (t) isSo g(t) =+

Answer 1

To create a linear model, we calculate the slope using two points for each function and identify the y-intercept by looking at the value when the independent variable is zero. Function f(t) has a slope of 30 and a y-intercept of 450, given by f(t) = 30t + 450. The linear system's solution represents the time when both functions have equal outputs.

Step-by-step explanation:

To create a linear model using the graph provided, we need to find the y-intercept and the slope for each function. For the function f(t), assume the coordinates given in the question are on the line for f(t). These points will allow us to calculate the slope (m). To find the y-intercept (b), we look at the value of f(t) when t (time) is zero.

Since we do not have specific values for the y-intercept and slope, let's take the points (0, 450) and (8, 690) for the function f(t). The slope m is calculated by the change in the vertical axis (rise) divided by the change in the horizontal axis (run). So here, the slope m would be (690 - 450) / (8 - 0) which equals 30. The y-intercept b is 450 as it is the output when t is 0, so f(t) = 30t + 450 for f(t).

For g(t), we need another point on the graph in addition to the y-intercept to calculate the slope. However, based on the provided graph, we can say g(t) has a y-intercept b at (0, 210) and we would calculate the slope in a similar manner once we have another point.

The linear system would then be created by setting the equations for f(t) and g(t) equal to each other and solving for t. The solution to this system represents the point in time t when the amount of apples picked by both functions is equal.

Answer 2

First we need to calculate the equation of f(x)

we need to calculated the slope m, using two points

(0,450)=(x1,y1)

(8,690)=(x2,y2)

`m=(y_2-y_1)/(x_2-x_1)=(690-450)/(8-0)=30`

m=30

the y-intercept b is where the line touches the y-axis in this case

b=450

the equation of the line is

`f(t)=30t+450`

The answers to the first 2 sentences are bold

The y-intercept, b, of f(t) is 450 and the slope, m, of f(t) is 30

So f(t) = 30t + 450.

In the case of g(x)

(0,210)=(x1,y1)

(8,690)=(x2,y2)

`m=(690-210)/(8-0)=(480)/(8)=60`

b=210

m=60

so the equation for g(x)=60x+210

The y-intercept, b, of g(t) is 210 and the slope, m, of g (t) is 60

So g(t) =60t+210

Part 2

The y-intercept represents the starting number of apples picked

The slope represents the number of apples picked per hour

The solution (8,690) represents a total of 690 apples each person gas after 8 hours