Question

amber created a scatter plot and drew a line of best fit, as shown.
what is the equation of the line of best fit that amber drew?

Explanation:

Step1: Identify the y-intercept

The line of best fit crosses the y - axis at (0, 12), so the y - intercept \(b = 12\).

Step2: Calculate the slope

We can use two points on the line. Let's take (0, 12) and (10, 15) (we can see that when \(x = 10\), the line passes through \(y=15\)). The slope formula is \(m=\frac{y_2 - y_1}{x_2 - x_1}\).
Substituting \(x_1 = 0,y_1 = 12,x_2=10,y_2 = 15\) into the formula: \(m=\frac{15 - 12}{10 - 0}=\frac{3}{10}=0.3\)

Step3: Write the equation of the line

The equation of a line in slope - intercept form is \(y=mx + b\), where \(m\) is the slope and \(b\) is the y - intercept. Substituting \(m = 0.3\) (or \(\frac{3}{10}\)) and \(b = 12\) into the formula, we get \(y = 0.3x+12\) (or \(y=\frac{3}{10}x + 12\))

Answer:

\(y = 0.3x+12\) (or \(y=\frac{3}{10}x + 12\))