Question

writing equations to model data

analyze the scatterplot and determine the equation that best models the data.

the relationship is dropdown
the rate of change is dropdown
the \\(y\\)-intercept is dropdown
the equation that models the data is dropdown

Explanation:

Identify the relationship type

Using the Linear Modeling knowledge point
The data points plotted on the scatterplot are:

$$ (0, 1), (1, 4), (2, 7), (3, 10), (4, 13), (5, 16), (6, 19), (7, 22), (8, 25) $$

Since these points lie perfectly on a straight line, the relationship is linear.

Calculate the rate of change

Using the Slope Formula and Average Rate of Change knowledge points

$$ m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{4 - 1}{1 - 0} = 3 $$

The rate of change is 3.

Determine the y-intercept

Using the Linear Modeling knowledge point
The line crosses the vertical axis at \( (0, 1) \).
The y-intercept is 1 (or the point \( (0, 1) \)).

Formulate the linear equation

Using the Linear Modeling knowledge point

$$ y = mx + b \implies y = 3x + 1 $$

The equation that models the data is \(y = 3x + 1\).

Answer:

Analyze the scatterplot and determine the equation that best models the data.
The relationship is <blank>linear</blank>.
The rate of change is <blank>3</blank>.
The y-intercept is <blank>1</blank> (or <blank>\((0, 1)\)</blank>).
The equation that models the data is <blank>\(y = 3x + 1\)</blank>.