Stephanie is working on a graph that represents the path of a roller coaster. The point (0, 840) represents the point at which the roller coaster first begins to drop at a constant rate. The point (15, 240) represents a point along the ride at which the roller coaster is still dropping. If the x-intercept represents the point at which the ride stops dropping, what is the x-intercept?
since y decreased by 600 when x increased by 15,
y = 840 - 40x
now solve for x when y=0
To find the x-intercept of the graph, we need to determine the point at which the roller coaster stops dropping.
Given the information, we know that the roller coaster drops at a constant rate from the point (0, 840) to the point (15, 240).
To find the rate at which the roller coaster drops, we can use the slope formula:
Slope = (y2 - y1) / (x2 - x1)
In this case, let's use (0, 840) for (x1, y1) and (15, 240) for (x2, y2):
Slope = (240 - 840) / (15 - 0)
= (-600) / 15
= -40
The negative value indicates that the roller coaster drops as we move along the x-axis.
Now that we have the slope, we can find the equation of the line that represents the path of the roller coaster. Using the point-slope form:
y - y1 = m(x - x1)
Using the point (0, 840) and the slope (-40):
y - 840 = -40(x - 0)
y - 840 = -40x
To find the x-intercept, we need to set y to zero and solve for x:
0 - 840 = -40x
-840 = -40x
Dividing both sides of the equation by -40:
x = -840 / -40
x = 21
Therefore, the x-intercept is 21.