Question

analyze the scatterplot and determine the equation that best models the data. the relationship is the rate of change is the y - intercept is the equation that models the data is y = 1/3x + 1 y = 1/3x - 1 y = 3x + 1 y = 3x - 1

Explanation:

Step1: Observe the scatter - plot trend

The points seem to form a linear pattern with a positive slope. So the relationship is linear and positive.

Step2: Estimate rate of change (slope)

Pick two points, say (0, 1) and (3, 2). The slope $m=\frac{y_2 - y_1}{x_2 - x_1}=\frac{2 - 1}{3-0}=\frac{1}{3}$.

Step3: Determine y - intercept

The line appears to cross the y - axis at the point (0, 1), so the y - intercept $b = 1$.

Step4: Find the equation

The slope - intercept form of a line is $y=mx + b$. Substituting $m=\frac{1}{3}$ and $b = 1$, we get $y=\frac{1}{3}x+1$.

Answer:

The relationship is linear and positive
The rate of change is $\frac{1}{3}$
The y - intercept is 1
The equation that models the data is $y=\frac{1}{3}x + 1$