Question

The table shows the outputs for several inputs. use two methods to find the output for an imput of 200

imputs: 0 1 2 3 4
outputs: 25 30 35 40 45
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Answer 1

Method 1 (Using Slope-Intercept Form):

First, we need to find the equation of the line that passes through the given points.

Slope (m) = (Change in y) / (Change in x) = (45 - 25) / (4 - 0) = 20 / 4 = 5

Using the slope and one point (0, 25), we can find the y-intercept:

y - y1 = m(x - x1)

y - 25 = 5(x - 0)

y = 5x + 25

Therefore, when the input is 200, the output would be:

y = 5(200) + 25

y = 1025

Method 2 (Using Linear Interpolation):

We can use the formula for linear interpolation:

y = y1 + ((x - x1) / (x2 - x1)) * (y2 - y1)

where:

x1 = 0, y1 = 25

x2 = 4, y2 = 45

x = 200

Substituting the values, we get:

y = 25 + ((200 - 0) / (4 - 0)) * (45 - 25)

y = 25 + (200 / 4) * 20

y = 25 + 500

y = 525

Therefore, when the input is 200, the output would be approximately 525.