Mathematics, 15.07.2020 01:01 jose145

The table of values represents a linear function g(x), where x is the number of days that have passed and g(x) is the balance in the bank account: x g(x) 0 $325 5 $400 10 $475 Part A: Find and interpret the slope of the function. (3 points) Part B: Write the equation of the line in point-slope, slope-intercept, and standard forms. (3 points) Part C: Write the equation of the line using function notation. (2 points) Part D: What is the balance in the bank account after 12 days? (2 points)

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Answer from: genyjoannerubiera

The balance in the bank account after 12 days is $505.

Step-by-step explanation:

The data provided is as follows:

Number of Days (x) Balance [g (x)]

0 $325

5 $400

10 $475

(a)

Compute the slope as follows:

$\sum{X} = 15 ~,~ \sum{Y} = 1200 ~,~ \sum{X \cdot Y} = 6750 ~,~ \sum{X^2} = 125$

$b &= \frac{ n \cdot \sum{XY} - \sum{X} \cdot \sum{Y}}{n \cdot \sum{X^2} - \left(\sum{X}\right)^2} = \frac{ 3 \cdot 6750 - 15 \cdot 1200 }{ 3 \cdot 125 - \left( 15 \right)^2} \approx 15\end{aligned}$

Thus, the slope of the function is 15.

The slope of a line is the rate of change in one variables that is caused by a unit change in the other variable.

In this case, the slope of the line implies that when one day has passed the balance in the bank account is increased by $15.

(b)

The point-slope form of the line is:

Consider the point (0, 325)

$y-0=15(x-325)\\\\y=15(x-325)$

The point-slope form is, y = 15 (x - 325)

Compute the intercept as follows:

$a &= \frac{\sum{Y} \cdot \sum{X^2} - \sum{X} \cdot \sum{XY} }{n \cdot \sum{X^2} - \left(\sum{X}\right)^2} = \frac{ 1200 \cdot 125 - 15 \cdot 6750}{ 3 \cdot 125 - 15^2} \approx 325 \\$

The slope intercept form of the line is:

$y=325+15\cdot x$

The standard form of the line is:

y-15x=325

(c)

The equation of the line using function notation is:

$g(x)=325+15\cdot x$

(d)

Compute the value of g (x) when x = 12 as follows:

$g(x)=325+15\cdot x$

$=325+(15\times 12)\\=325+180\\=505$

Thus, the balance in the bank account after 12 days is $505.

Answer from: howey74

A)The slope of function is 15

B) Point slope form :

Slope-intercept form : y=15x+325

Standard form: 15x+y=325

C)g(x)=15x+325

D) The balance in the bank account after 12 days is $505

Step-by-step explanation:

x g(x)

0 $325

5 $400

10 $475

Part A: Find and interpret the slope of the function.

Formula of slope = $m = \frac{y_2-y_1}{x_2-x_1}$

We are given that

$(x_1,y_1)=(0,325)\\(x_2,y_2)=(5,400)$

Substitute the values in the formula:

$m=\frac{400-325}{5-0}$

m=15

So, The slope of function is 15

Part B: Write the equation of the line in point-slope, slope-intercept, and standard forms.

Point slope form : y-y_1=m(x-x_1)

y-325=15(x-0)

Slope-intercept form = y=mx+c

y=15x+325

Standard form : Ax+By=C

So, -15x+y=325

Part C: Write the equation of the line using function notation.

g(x)=15x+325

Part D: What is the balance in the bank account after 12 days?

Substitute x = 12

So, g(x)=15(12)+325

g(x)=505

Hence the balance in the bank account after 12 days is $505

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