Question

Suppose the following function is graphed. y=8/5x+4 On the same grid, a new function is graphed. The new function is represented by the following equation. y=-5/8x+8. Which of the following statements about these graphs is true? A. The graphs intersect at (0,8). B. The graph of the original function is perpendicular to the graph of the new function. C. The graph of the original function is parallel to the graph of the new function. D. The graphs intersect at (0,4).

Answer 1

Hey mate,

On the x Axis.

Explanation :

In the given picture.

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Answer 2

Answer:

Option (B) The graph of the original function is perpendicular to the graph of the new function is the correct answer.

A) False

B) True

C) False

D) False

Step-by-step explanation:

The graph of $y = \frac{8x}{5}+4 and y = \frac{5x}{8}+8$ are shown in the figure.

A) The graphs intersect at (0,8) is False.

The graphs intersect at (1.79, 6.87)

Calculation:

• If two lines intersect each other there will be a common point for both lines.

• This common point can be calculated by solving the equations of two lines.

Line 1: $y = \frac{8x}{5}+4$

Line 2: $y = \frac{-5x}{8} +8$

By equating the R.H.S of two equations since the L. H. S are equal,

$\frac{8x}{5}+4 = \frac{-5x}{8}+8\\ \\ \frac{8x}{5}+\frac{5x}{8} = 4\\\\\frac{64x+25x}{40} = 4\\ \\89x = 160\\\\x = 1.79$

Substituting value of x in Line 1 equation,

$y = \frac{8*1.79}{5}+4\\ \\y = 6.87$

B) The graph of the original function is perpendicular to the graph of the new function is True.

From the properties of perpendicular lines, the product of slopes of perpendicular lines is -1.

Slope of line in the form y = mx + c is m.

Slope of line 1 is 8/5

Slope of line 2 is - 5 / 8

Product of slopes = $\frac{8}{5} * \frac{-5}{8} = -1$

C) The graph of the original function is parallel to the graph of the new function is False as they are perpendicular to each other.

D) The graphs intersect at (0,4) is False as they intersect at (1.79, 6.87)

Find more about lines:

Parallel and Perpendicular lines

https://brainly.in/question/48103092

Properties of straight lines

https://brainly.in/question/47092640