Question

Plz help me........................................................

Answer 1

Answer:

Please check the explanation.

Step-by-step explanation:

Question 1)

Input, x                            Output, y

0                                       0

1                                         4

2                                        8

3                                       12

It is clear that the values of input 'x' and output 'y' are changing in constant proportions. It means the rate of change must be constant. Thus, this represents a linear function.

Finding the slope between (0, 0) and (1, 2)

slope = m = y₂-y₁ / x₂-x₁

                 = (2-0) / (1-0)

                  = 2 / 1

                  = 2

Thus, the slope = m = 2

We know that the y-intercept can be obtained by setting x = 0 and solving for y.

It is clear at x = 0, y = 0

Thus, the y-intercept b = 0

We know that the slope-intercept form of linear equation

y = mx+b

substitute m = 2 and b = 0

y = 2x + 0

y = 2x

Thus, the equation that describes the equation is:

y = 2x

Question 2)

The output is eleven more than the input.

As 'y' represents the output.

'x' represents the input.

so

y = x+11

Question 3)

The output is the cube of the input.

As 'y' represents the output.

'x' represents the input.

so

y = x³

Question 4)

The output is one more than twice the input.

As 'y' represents the output.

'x' represents the input.

so

y = 2x+1

Question 5)

y = 7x

substitute x = -5

y = 7(-5)

y = -35