Question

I need help finding the slope, identifying the initial value and writing An equation for a linear function and finding the X answer Y intercept PLEASE HELP PLEASE ​

Answer 1

Answer/Step-by-step explanation:

✔️Slope (m) using the two points (2, 4.58) and (5, 4.28):

$slope (m) = \frac{y_2 - y_1}{x_2 - x_1} = \frac{4.28 - 4.58}{5 - 2} = \frac{-0.3}{3} = -0.1$

Slope (m) = -0.1

✔️Initial Value = y-intercept = b

To find b, substitute x = 2, y = 4.58, and m = -0.1 into y = mx + b.

(Note: y is P(t) and x is t).

Thus:

4.58 = (-0.1)(2) + b

4.58 = -0.2 + b

Add 0.2 to both sides

4.58 + 0.2 = b

4.78 = b

b = 4.78

Initial value = 4.78

✔️Equation for the linear function:

Substitute b = 4.78, and m = -0.1 into P(t) = mt + b

Thus the equation would be:

P(t) = -0.1t + 4.78

✔️The y-intercept = initial value = 4.78

✔️The x-intercept = the value of t when P(t) = 0.

To get this, substitute P(t) = 0 into P(t) = -0.1t + 4.78.

Thus:

0 = -0.1t + 4.78

Add 0.1t to each side

0.1t = 4.78

Divide both sides by 0.1

t = 47.8

x-intercept = 47.8