Question

1. determine the equation for the line of best fit.

a scatter plot was constructed on the graph below and a line of best fit was drawn.
step 1: identify the y-intercept
step 2: use two points on the trend line to calculate the slope (hint: (1, 30), (2, 35), and (7, 60) are great points to use in a table! remember to do change in y divided by change in x
step 3: write the equation $y = mx + b$

Explanation:

Step 1: Identify the y - intercept

The y - intercept \(b\) is the value of \(y\) when \(x = 0\). From the hint and the general form of the line \(y=mx + b\), we can also observe from the trend line. Let's assume from the graph (or the hint) that when \(x = 0\), the y - intercept \(b=25\) (we can also check with the points given. Let's verify with the point \((1,30)\) later).

Step 2: Calculate the slope

We use two points on the trend line. Let's take the points \((1,30)\) and \((2,35)\). The formula for slope \(m=\frac{y_2 - y_1}{x_2 - x_1}\).
Substituting \(x_1 = 1,y_1 = 30,x_2=2,y_2 = 35\) into the formula:
\(m=\frac{35 - 30}{2 - 1}=\frac{5}{1}=5\)

Step 3: Write the equation of the line

The general form of a linear equation is \(y=mx + b\), where \(m\) is the slope and \(b\) is the y - intercept. We found that \(m = 5\) and \(b=25\). So the equation of the line of best fit is \(y = 5x+25\)

Answer:

The equation of the line of best fit is \(y = 5x + 25\)