Question

TUZ.U410)

Answer 1

Answer:

Part A: 15

Part B:

Point slope form: $y-400=15(x-5)$

Slope intercept form: $y =15x+325$

Standard Form: $15x-y+325=0$

Part C: $g(x) =15x+325$

Part D: 505

Step-by-step explanation:

We are given the following

x       g(x)

5      $400

10    $475

We can see that these are two points on the line.

i.e. (5, 400) and (10, 475)

OR

$x_1 = 5\\x_2 = 10\\y_1 = 400\\y_2 = 475$

Part A: Slope of the function:

$m=\dfrac{y_2-y_1}{x_2-x_1} \\\Rightarrow m = \dfrac{475-400}{10-5}\\\Rightarrow m = \dfrac{75}{5} = 15$

So, slope of the line = 15

It has a positive slope and the function will be increasing with the increasing value of 'x'.

Part B:

Point slope form of a line is given as:

$y-y_1=m(x-x_1)$

Putting $(x_1, y_1)\ as\ (5, 400)$:

$y-400=15(x-5)$

Slope intercept form:

$y=mx+c$ where c is the intercept.

$y =15x+c$

Putting (x,y) as (5, 400) to find c:

$400=15\times5+c\\\Rightarrow c = 325$

So, the equation in slope intercept form:

$y =15x+325$

Standard form of line:

$Ax+By+C=0$

Rewriting the slope intercept form:

$15x-y+325=0$

Part C:

Using the function notation, putting y = g(x) in slope intercept form:

$g(x) =15x+325$

Part D:

Balance after 12 days = ?

i.e. g(x) = ? at x = 12

Putting x = 12 in $g(x) =15x+325$

$g(12) =15\times 12+325\\\Rightarrow g(12)=505$