an investor purchased a house 8 years ago for $48,000. this year it was appraised at $74,500. complete parts…

an investor purchased a house 8 years ago for $48,000. this year it was appraised at $74,500. complete parts (a) through (d) below.\n(a) a linear equation v = mt + b, 0 ≤ t ≤ 15, represents the value v of the house for 15 years after it was purchased. determine m and b.\nm = 3187.5\nb = 44000\n(type integers or decimals.)

an investor purchased a house 8 years ago for $48,000. this year it was appraised at $74,500. complete parts (a) through (d) below.\n(a) a linear equation v = mt + b, 0 ≤ t ≤ 15, represents the value v of the house for 15 years after it was purchased. determine m and b.\nm = 3187.5\nb = 44000\n(type integers or decimals.)

Answer

Explanation:

Step1: Find the slope m

We know two points on the line: when $t = 0$ (at the time of purchase), $V=48000$; when $t = 8$, $V = 74500$. The slope formula for a line $V=mt + b$ is $m=\frac{V_2 - V_1}{t_2 - t_1}$. Substituting $V_1 = 48000$, $t_1=0$, $V_2 = 74500$, $t_2 = 8$ into the formula, we get $m=\frac{74500 - 48000}{8-0}=\frac{26500}{8}=3312.5$.

Step2: Find the y - intercept b

When $t = 0$ (the time of purchase), substituting into the equation $V=mt + b$, we have $V=b$. Since the initial value of the house when $t = 0$ is $48000$, so $b = 48000$.

It seems there is an error in the provided answers in the image.

Answer:

$m = 3312.5$, $b=48000$