Mathematics, 01.03.2021 15:30, leasincobe4327

Graph the equations Y=400+50x
Y=300+25x

1.) from the graph at what time will the they have the same height

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Graph the equations

Y=400+50x
Y=300+25x
1.) from the graph at what time will the they have the sa

Answers: 3

Show answers

Answers

answered: maybe67

We conclude that, at 4 minutes, both will have the same height which is 200 feet.

Step-by-step explanation:

Given the system of equations

y=400+50x

y=300+25x

Important Tip:

The point of intersection of the two lines would give us the point at which both have the same height.

Graphing the system of equations

The graph of the equation y = 400 + 50x

First, determine the y-intercept of the equation y = 400 + 50x by substituting x = 0

y = 400 + 50x

y = 400 + 50(0)

y = 400 + 0

y = 400

Thus, we determine that the ordered pair (0, 400) represents the y-intercept of the equation y = 400 + 50x.

Next, determine the x-intercept of the graph of the equation y = 400 + 50x by substituting y = 0

y = 400 + 50x

0=400+50x

switch sides

400+50x=0

Subtract 400 from both sides

400+50x-400=0-400

Simplify

50x=-400

Divide both sides by 50

$\frac{50x}{50}=\frac{-400}{50}$

Simplify

x=-8

Thus, we determine that the ordered pair (-8, 0) represents the x-intercept of the equation y = 400 + 50x.

Important Tip:

The point at which the graph crosses the y-axis is called the y-intercept. The point at which the graph crosses the x-axis is called the x-intercept.

The red graph on the diagram represents the equation y = 400 + 50x having the y-intercept (0, 400) and x-intercept (-8, 0)

Please check the attached diagram.

The graph of the equation y = 300 + 25x

Now, determine the y-intercept of the equation y = 300 + 25x by substituting x = 0

y = 300 + 25x

y = 300 + 25(0)

y = 300 + 0

y = 300

Thus, we determine that the ordered pair (0, 300) represents the y-intercept of the equation y = 300 + 25x.

Next, determine the x-intercept of the graph of the equation y = 300 + 25x by substituting y = 0

y=300+25x

0 = 300 + 25x

switch sides

300+25x=0

Subtract 300 from both sides

300+25x-300=0-300

Simplify

25x=-300

Divide both sides by 25

$\frac{25x}{25}=\frac{-300}{25}$

Simplify

x=-12

Thus, we determine that the ordered pair (-12, 0) represents the x-intercept of the equation y = 300 + 25x.

The blue graph on the diagram represents the equation y = 300 + 25x having the y-intercept (0, 300) and x-intercept (-12, 0)

Please check the attached diagram.

Analyze the POINT OF INTERSECTION:

As we already know that the point of intersection of the two lines would give us the point at which both have the same height.

The diagram indicates that:

at x = -4, the value of y = 200.

It is the point where both lines meet.

Thus, the point of intersection of the two lines is:

(x, y) = (-4, 200)

Conclusion:

As x represents the time in minutes and y represents the height in feet.

Thus, we conclude that at x = 4 minutes, both will have the same height i.e. y = 200 feet

Therefore, we conclude that, at 4 minutes, both will have the same height which is 200 feet.

Graph the equations

Y=400+50x
Y=300+25x
1.) from the graph at what time will the they have the same

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Graph the equations Y=400+50x
Y=300+25x

1.) from the graph at what time will the...