Question

match the data to its corresponding line of best fit.
x -20 -11 -7 5
y 66 39 27 -9
(-1, 2), (0.5, 4), (2, 5), (3, 20)
x 4 5 6 7
y 1.88 2.35 2.82 3.29
(0, 6), (2,3), (3,4), (5,3)
y is 6 when x is 2, y is 9 when x is 5, and y is 17 when x is 8.
x 0 2 4 6
y 5 4 1 2
y is 6 when x is 0, y is 1 when x is 2, and y is 5 when x is 4.
(1, 1.5), (2, 0.8), (4, 3.5), (5,2)
answer choices
y = -0.6x + 4.8
y = 3.82x + 3.45
y = -3x + 6
y = -0.25x + 4.5
y = 0.37x + 0.84
y = -0.54x + 5.35
y = 0.47x
y = 1.83x + 1.5

Explanation:

Step1: Recall slope - intercept form

The equation of a line is $y=mx + b$, where $m$ is the slope and $b$ is the y - intercept.

Step2: Calculate slope for each data set

For two points $(x_1,y_1)$ and $(x_2,y_2)$, the slope $m=\frac{y_2 - y_1}{x_2 - x_1}$.

Step3: Estimate y - intercept

We can use one of the points $(x,y)$ from the data set and the calculated slope $m$ in the equation $y=mx + b$ to solve for $b$ ($b=y - mx$).

Step4: Match with answer choices

Compare the calculated equations $y=mx + b$ with the given answer choices to find the best - fit line. For example, for the first data set with points $(-20,66)$ and $(-11,39)$:

• Calculate slope $m=\frac{39 - 66}{-11+20}=\frac{-27}{9}=-3$.
• Using the point $(-20,66)$ and $m = - 3$ in $y=mx + b$, we get $66=-3\times(-20)+b$, so $b = 66 - 60=6$. The equation is $y=-3x + 6$.

Answer:

1. For the data

$$\begin{matrix}X& - 20&-11&-7&5\\Y&66&39&27& - 9\end{matrix}$$

: $y=-3x + 6$

1. For the data $(-1,2),(0.5,4),(2,5),(3,20)$: $y = 3.82x+3.45$
2. For the data

$$\begin{matrix}X&4&5&6&7\\Y&1.88&2.35&2.82&3.29\end{matrix}$$

: $y=0.47x$

1. For the data $(0,6),(2,3),(3,4),(5,3)$: $y=-0.25x + 4.5$
2. For the data where $y$ is $6$ when $x$ is $2$, $y$ is $9$ when $x$ is $5$, and $y$ is $17$ when $x$ is $8$: $y = 1.83x+1.5$
3. For the data

$$\begin{matrix}X&0&2&4&6\\Y&5&4&1&2\end{matrix}$$

: $y=-0.54x + 5.35$

1. For the data where $y$ is $6$ when $x$ is $0$, $y$ is $1$ when $x$ is $2$, and $y$ is $5$ when $x$ is $4$: $y=-0.6x + 4.8$
2. For the data $(1,1.5),(2,0.8),(4,3.5),(5,2)$: $y=-0.25x + 4.5$