Question

Assessment items Mrs. Sheng has two batches of bamboo plants that she will use to make a fence with poles of similar heights. When she transplanted the plants, the first batch, which grows at a rate of 2 ft/week, had stalks that were about 4 ft high. The second batch, which grows at a rate of 1.5 ft/week, had stalks that were about 7 ft high. The equation y=2x+4 y=2x+4 models the height, y, of the plants in the first batch x weeks after they were transplanted. The equation y= 3 2 x+7 y=32x+7 models the height, y, of the plants in the second batch x weeks after they were transplanted. Graph the system formed by the equations.

Answer 1

Answer: The below graph shows the given situation.

Explanation:

Here x represents the number of week and y represents the total height f the plant after x weeks.

Then, According to the question,

For the first batch,

y = 2x + 4 ------ (1)

Which is the line having the x-intercept = (-2,0)

And, y-intercept = (0,4)

And, For the second batch,

y = 1.5x + 7

y = 3x/2 + 7 -------(2)

Which is a line that having x-intercept = (-14/3,0)

And, y-intercept = (0,7)

By solving equation (1) and (2),

We get,

x = 6 and y = 16

That is, the intersection point of line (1) and (2) is (6,16)

Thus, By the above explanation we can plot the solution of the system of equations (1) and (2) in the graph.