What point on the graph of y = 0.5f(x) corresponds to (4, 16)? Explain.

Mathematics

1 answer:

SVETLANKA909090 [29]3 years ago

4 0

We are given a coordinate (4,16).

Where first coordinate is the value of x and second coordinate is the value of y for the function y=f(x).

We need to find the value of given point (4,16) for function y= 0.5f(x).

Here function f(x) is being multiplied by 0.5.

On multiplying 0.5 by y, it will effect the value of y only. It does not effect value of x . Because x value is still x. Only function f(x) is being multiplied by 0.5.

Therefore, y= 0.5f(4) = 0.5 * 16 = 8.

So, (4,8) is the point on the graph of y = 0.5f(x) corresponds to (4, 16).

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A student created this table to represent a linear relationship between x and y.X Y-2. 10.0-1. 7.50. 5.01. 2.52. 0The student sa

alex41 [277]

The relationship between x and y is represent as:

Since, the relationship is linear.

The standard form of equation of line is:

$y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)$

Consider any two set x and y values from the given relationship.

Let (-2, 10) and (-1,7.5)

$\text{Substitute x}_1=-2,y_1=10,x_2=-1,y_2=7.5\text{ in the standard equation of line.}$

$\begin{gathered} y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1) \\ y-10=\frac{7.5-10}{-1-(-2)}(x-(-2)) \\ y-10=\frac{-2.5}{1}(x+2) \\ y-10=-2.5(x+2) \\ y=-2.5(x+2)+10 \end{gathered}$

The equation of the linear relationship between x and y is:

y = -2.5(x + 2) + 10

Now, to check that the point (9, -17.5) lies on the represented relationship between x and y

Substitute x = 9 and y = -17.5 in the equation y = -2.5(x + 2) + 10

y = -2.5(x + 2) + 10

-17.5 = -2.5(9 + 2) + 10

-17.5 = -2.5(11) + 10

-17.5 = -27.5 + 10

-17.5 = -17.5

Thus, LHS = RHS

Hence the point (9, -17.5) lie on the given linear relationship between x and y.

Answer: The point (9, -17.5) lie on the given linear relationship between x and y.