## a linear function passes through the point (1,5)and (7,23)what are the rate of change and initial value?

Question

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## Answers ( )

Answer:The rate of change = 3

Initial value = 2

Step-by-step explanation:The linear function has the form ⇒ y = mx + c

Where m is the slope or the rate of change, and c is y-intercept.

Given: A linear function passes through the point (1,5)and (7,23)

So, m = (y₂-y₁)/(x₂-x₁) = (23-5)/(7-1) = 18/6 = 3

So, y = 3x + c

By substitution with the point (1,5)

So, at x = 1 , y = 5

5 = 3*1 + c

c = 5 – 3 = 2

∴ y = 3x + 2

so, the rate of change = 3

And initial value = 2initial value is the value at which x = 0 which is the y-intercept