Question

use the following information to answer questions 3 - 4. hector spent the summer gardening. the amount of money he earned, and the hours is shown in the scatterplot. 3. choose two points on the line and determine which equation best represents the trend line. a. y = 1.67x + 1 b. y = 1.50x + 1 c. y = 2x + 1 d. y = 1.33x + 1

Explanation:

Step1: Recall slope - intercept form

The equation of a line is $y = mx + b$, where $m$ is the slope and $b$ is the y - intercept. The y - intercept is the value of $y$ when $x = 0$. Looking at the scatter - plot, the line seems to cross the y - axis around $y = 1$, so $b=1$.

Step2: Calculate slope approximation

To find the slope $m$, we can choose two points on the line. Let's assume two points $(x_1,y_1)$ and $(x_2,y_2)$. If we take two well - aligned points on the trend line, say $(1,2.67)$ and $(2,4.33)$. The slope $m=\frac{y_2 - y_1}{x_2 - x_1}=\frac{4.33 - 2.67}{2 - 1}=1.66\approx1.67$.

Step3: Determine the equation

Since $m\approx1.67$ and $b = 1$, the equation of the line is $y=1.67x + 1$.

Answer:

A. $y = 1.67x+1$