Question

1. find the equation of the line containing the first and the last data points.

1. what is the equation of the line of best fit for the data in the table (use graphing calculator)?

final equation__________________________

Explanation:

Step1: Find the slope for problem 12

The first data point is \((-2,-4)\) and the last is \((2,5)\). The slope formula is \(m=\frac{y_2 - y_1}{x_2 - x_1}\).

$$m=\frac{5-(-4)}{2-(-2)}=\frac{5 + 4}{2+2}=\frac{9}{4}$$

Step2: Use the point - slope form for problem 12

Using the point - slope form \(y - y_1=m(x - x_1)\), take the point \((-2,-4)\) and \(m = \frac{9}{4}\).

$$y+4=\frac{9}{4}(x + 2)$$

$$y+4=\frac{9}{4}x+\frac{9}{2}$$

$$y=\frac{9}{4}x+\frac{9}{2}-4$$

$$y=\frac{9}{4}x+\frac{9 - 8}{2}$$

$$y=\frac{9}{4}x+\frac{1}{2}$$

Step3: Use a graphing calculator for problem 13

Input the \(x\) - values \(\{1,2,5,8,9,17\}\) and \(y\) - values \(\{30,55,75,120,145,250\}\) into a graphing calculator. Run the linear regression (LinReg) function.
The general form of a linear regression equation is \(y=ax + b\). After running LinReg on the calculator, we get \(a\approx13.04\) and \(b = 16.43\)

Answer:

1. \(y=\frac{9}{4}x+\frac{1}{2}\)
2. \(y = 13.04x+16.43\)