Question

How do i determine which of these fit the graph data?d(t)=50t+300d(t)=50td(t)=-50t+300d(t)=-50t

Answer 1

To determine the behavior of the graph, we calculate the slope-intercept form of the graph. It is given by

y = mx + b

Here, b is the y-intercept.

m is the slope of the graph that is the difference between y-axis over x-axis.

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

To calculate both points, let's pick two points from the graph.

For example, the first point is (1, 250) and the second point is (2, 200)

So,

(x1, y1) = (1, 250)

x1 = 1

y1 = 250

(x2, y2) = (2, 200)

x2 = 2

y2 = 200

Now, put these values in slope form, we get

m = (200 - 250) / (2 - 1)

m = -50

Hence, the slope is -50 that tells that with every on increase in the value of x, y is decreasing 50. Hence, if I decrease the value of x, y will rise 50.

Therefore,

I can say that when x = 0, y = 300. (0, 300)

Therefore, b = 300

Now, put all these values in the slope-intercept form.

y = mx + b

dt = -50x + 300

Hence, the 3rd option is correct.