Question

raquel throws darts at a coordinate grid centered at the origin. her goal is to create a line of darts. her darts actually hit the coordinate grid at (-5, 0), (1, -3), (4, 5), (-8, -6), (0, 2), and (9, 6). which equation best approximates the line of best fit of the darts?
y = 0.6x + 0.6
y = 0.1x + 0.8
y = 0.8x + 0.1
y = 0.5x + 0.6

Explanation:

Step1: Recall the form of a linear regression line

The line of best - fit for a set of data points has the form $y = mx + b$, where $m$ is the slope and $b$ is the y - intercept. One way to estimate is to use the fact that for a set of points $(x_i,y_i)$, the least - squares regression line can be approximated by considering the general trends of the data. We can also use a graphing utility or a statistical software. Another way is to make a rough estimate by looking at the rise and run between points and the general position of the line relative to the y - axis.
We can take two points and estimate the slope $m=\frac{y_2 - y_1}{x_2 - x_1}$ and then estimate the y - intercept by looking at where the line would cross the y - axis.
Let's take two points, say $(0,2)$ and $(4,5)$.

Step2: Calculate the slope

The slope $m=\frac{y_2 - y_1}{x_2 - x_1}=\frac{5 - 2}{4-0}=\frac{3}{4}=0.75\approx0.8$.
The y - intercept is the y - value when $x = 0$. We have the point $(0,2)$, so the y - intercept $b\approx0.1$ is a reasonable estimate when considering the overall trend of the data points.

Answer:

C. $y = 0.8x+0.1$