Question

click the icon to view the data table. complete parts (a) through (c).
(a) draw a scatter diagram treating x as the explanatory variable and y as the response variable. choose the correct graph below.
a.
b.
c.
d.
(b) find the equation of the line containing the points (-2, -2) and (2,5).
the equation of the line is y = □x + □.

Explanation:

Step1: Calculate the slope \(m\)

The formula for the slope \(m\) between two points \((x_1,y_1)\) and \((x_2,y_2)\) is \(m=\frac{y_2 - y_1}{x_2 - x_1}\).
Given \((x_1,y_1)=(-2,-2)\) and \((x_2,y_2)=(2,5)\), then \(m=\frac{5-(-2)}{2-(-2)}=\frac{5 + 2}{2+2}=\frac{7}{4}\).

Step2: Use the point - slope form \(y - y_1=m(x - x_1)\)

Using the point \((x_1,y_1)=(-2,-2)\) and \(m = \frac{7}{4}\), we have \(y-(-2)=\frac{7}{4}(x-(-2))\).
Simplify the equation: \(y + 2=\frac{7}{4}(x + 2)\).
Expand the right - hand side: \(y+2=\frac{7}{4}x+\frac{7}{2}\).
Subtract 2 from both sides: \(y=\frac{7}{4}x+\frac{7}{2}-2\).
Since \(2=\frac{4}{2}\), then \(y=\frac{7}{4}x+\frac{7 - 4}{2}=\frac{7}{4}x+\frac{3}{2}\).

Answer:

The equation of the line is \(y = \frac{7}{4}x+\frac{3}{2}\).