Answer:
Please check the explanation.
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