Chapter 8, Problem 13STP

To determine

The equation in slope-intercept form of the equation.

Answer to Problem 13STP

The slope-intercept form of the equation is $V=365t-713975$

Explanation of Solution

Given information:

Ordered pair $\left(t_1,V_1\right)=(1995,14200)$ and $\left(t_2,V_2\right)=(2003,17120)$

Calculation:

Let $t$ represents the year and $V$ represents the cost of painting.

Mr. C bought a painting in 1995 for $\text{\$}14.200$

So the ordered pair is $\left(t_1,V_1\right)=(1995,14200)$

In 2003 , the painting was 517,120 . So the ordered pair is $\left(t_2,V_2\right)=(2003,17120)$

Write the equation of the line that passes through (1995,14200) and (2003,17120)

Determine the slope of the line.

  $\begin{array}{cc}m& =\frac{V_2-V_1}{t_2-t_1}\\ & =\frac{17120-14200}{2003-1995}\\ & =\frac{2920}{8}\\ & =365\end{array}$ Slope formula

Choose (1995,14200) and find the $y-$ intercept of the line.

  $V=mt+b$ Slope-intercept form

  $\begin{array}{cc}14200& =365(1995)+b\\ 14200& =728175+b\\ b& =-713975\end{array}$

Write the equation using $m=365$ and $b=-713975$

  $V=365t-713975$

Check:

Check the result by using the coordinates of (2003,17120).

  $V=365t-713975$

  $17120=365(2003)-713975$

  $17120=731095-713975$

  $17120=731095-713975$

Therefore, the slope-intercept form of the equation is $V=365t-713975$