Question

Graph the equations

Answer 1

Answer:

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.