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

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 = 2

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

the ratio of white tiles to blue tiles is 48: 16. the ratio in it's simplest form is 3: 1.

step-by-step explanation:

ratio: take the first number and add a colon next to it, then add the second number after that. make sure the ratio order matches up with the written problem!

simplest form: we can simplify the ratio 48 : 16 by dividing both terms by the greatest common factor (gcf).

the gcf of 48 and 16 is 16.

divide both terms by 16:

48 ÷ 16 = 3

16 ÷ 16 = 1

reducing to simplest form:

48 : 16 = 3 : 1

answer is 144

step-by-step explanation: