Question

GIVING 100 POINTS: The graph shown here displays the distance, in miles. traveled by a jet in a certain number of hours. Based on the graph, which of the following equations indicates the correct variables, and in how many hours does the jet travel 12,000 miles if it travels at the same speed?

Graph titled Motion of a Jet shows Time in hours on x axis and Distance in miles on y axis. A straight line joins the ordered pairs 0, 0 and 2, 1200 and 4, 2400 and 6, 3600.

y = 600x, the jet travels 12,000 miles in 20 hours
x = 600y, the jet travels 12,000 miles in 20 hours
y = 600x, the jet travels 12,000 miles in 22 hours
x = 600y, the jet travels 12,000 miles in 22 hours

Answer 1

A. y = 600x, the jet travels 12,000 miles in 20 hours

Step-by-step explanation:

`\sf slope: (y_2 - y_1)/(x_2- x_1) \ \ where \ (x_1 , \ y_1), ( x_2 , \ y_2) \ are \ points`

Take two points: (2, 1200), (4, 2400)

`\sf slope : (2400-1200)/(4-2 ) = 600`

Equation:

y - 1200 = 600(x - 2)

y - 1200 = 600x - 1200

y = 600x

Miles the Jet travels at 20 hours:

• y = 600(20) = 12000 miles

Miles the Jet travels at 22 hours:

• y = 600(22) = 13200 miles

Answer 2

y = 600x, the jet travels 12,000 miles in 20 hours

Step-by-step explanation:

Slope-intercept form of a linear equation:

`y = mx + b`

where:

• m = slope
• b = y-intercept

To find the slope, define two points on the line and use the slope formula to find the slope:

• 
  `\textsf{let}\:(x_1,y_1)=(0,0)`

• 
  `\textsf{let}\:(x_2,y_2)=(2, 1200)`

`\implies \textsf{slope}\:(m)=(y_2-y_1)/(x_2-x_1)=(1200-0)/(2-0)=600`

From inspection of the graph, the y-intercept (where the line crosses the y-axis) is at (0, 0). Therefore, the equation of the line is:

y = 600x

y is defined as the distance (in miles). Therefore, to find the number of hours it takes for the jet to travel 12,000 miles, substitute y = 12000 into the found equation and solve for x:

`\sf \implies 600x=12000`

`\sf \implies x=(12000)/(600)`

`\sf \implies x=(120)/(6)`

`\implies \sf x=20`

Therefore, it takes the jet 20 hours to travel 12,000 miles.