Question

pretest: special linear relationships
what is the equation of the line of best fit that amber drew?
a. $y = 3x + 12$
b. $y = 3x + 15$
c. $y = \frac{1}{3}x + 12$
d. $y = \frac{1}{3}x + 15$

Explanation:

Step1: Identify the y-intercept

The line of best fit crosses the y-axis at \( x = 0 \). From the graph, when \( x = 0 \), \( y = 12 \). So the y-intercept (\( b \)) is 12.

Step2: Calculate the slope

We can use two points on the line. Let's take \( (0, 12) \) and another point, say \( (3, 13) \) (or observe the rise over run). The slope (\( m \)) is calculated as \( \frac{\text{change in } y}{\text{change in } x} \). From \( x = 0 \) to \( x = 3 \), \( y \) changes from 12 to 13? Wait, no, looking at the options, the slope is \( \frac{1}{3} \). Let's check: if \( x = 3 \), \( y = \frac{1}{3}(3) + 12 = 1 + 12 = 13 \), which matches the trend. So the slope \( m = \frac{1}{3} \) and y-intercept \( b = 12 \). So the equation is \( y = \frac{1}{3}x + 12 \).

Answer:

C. \( y = \frac{1}{3}x + 12 \)