Question

heather used a graphing utility to find the equation of the line of best fit in this scatter plot.

Explanation:

Step1: Identify two points on the line

We can take the y - intercept (0, 1.5) and another point, say (2, 3).

Step2: Calculate the slope (m)

The slope formula is $m=\frac{y_2 - y_1}{x_2 - x_1}$. Using (0, 1.5) as $(x_1,y_1)$ and (2, 3) as $(x_2,y_2)$, we get $m=\frac{3 - 1.5}{2 - 0}=\frac{1.5}{2}=0.75=\frac{3}{4}$.

Step3: Write the equation of the line

Using the slope - intercept form $y = mx + b$, where $m=\frac{3}{4}$ and $b = 1.5=\frac{3}{2}$. So the equation is $y=\frac{3}{4}x+\frac{3}{2}$.

Answer:

The equation of the line of best fit is $y = \frac{3}{4}x+\frac{3}{2}$ (or in decimal form $y = 0.75x+1.5$)