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

1. can there be more than one point of intersection between the graphs of two linear equations? explain.

Explanation:

Step1: Find the slope (m)

The first data point is \((x_1,y_1)=(-2,-4)\) and the last data point is \((x_2,y_2)=(2,5)\).
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 \(y - y_1=m(x - x_1)\)

Using the point \((x_1,y_1)=(-2,-4)\) and \(m=\frac{9}{4}\)

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

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

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

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

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

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

Answer:

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