A graph is shown with 4 dots

Question

Dot 1: (-4, 0)
Dot 2: (-2, 1)
Dot 3: (0, 2)
Dot 4: (2, 3)
Answer the questions from the graph.

(4 points)
Put responses in the correct input to answer the question. Select a response, navigate to the desired input and insert the response. Responses can be selected and inserted using the space bar, enter key, left mouse button or touchpad. Responses can also be moved by dragging with a mouse.
What is the y-intercept? Response area

What is the slope? Response area

What is the equation of the line in slope-intercept form? Response area

This is a Response area relationship.

Answer 1

To answer your questions based on the graph with the four dots provided:

1. What is the y-intercept? From the points given, the y-intercept is the value of y when x = 0. In this case, Dot 3 (0, 2) indicates that the y-intercept is 2.

2. What is the slope? The slope \( m \) can be calculated using any two points from the graph, typically using the formula: \[ m = \frac{y_2 - y_1}{x_2 - x_1} \] Let's take Dot 3 (0, 2) and Dot 4 (2, 3): \[ m = \frac{3 - 2}{2 - 0} = \frac{1}{2} \] Therefore, the slope is 1/2.

3. What is the equation of the line in slope-intercept form? The slope-intercept form of the equation of a line is given by: \[ y = mx + b \] where \( m \) is the slope and \( b \) is the y-intercept. Substituting in the values: \[ y = \frac{1}{2}x + 2 \] Thus, the equation of the line is y = (1/2)x + 2.

4. This is a Response area relationship.
   The relationship here indicates how the points are connected on a linear graph, with the slope showing the rate of change and the y-intercept indicating where the line crosses the y-axis.

You can fill in the response areas with the collected answers:

• Y-intercept: 2
• Slope: 1/2
• Equation of the line in slope-intercept form: y = (1/2)x + 2

Answer 2

what type of relationship is it?

Answer 3

The relationship represented by the points provided is a linear relationship. This is indicated by the fact that the points can be connected by a straight line, which means that there is a constant rate of change (the slope) between the variables. In summary:

• Type of relationship: Linear relationship

This means that for every unit increase in the x-coordinate, the y-coordinate increases by a constant amount (in this case, \( \frac{1}{2} \) per unit increase in x).

Answer 4

the options are proportional, non proportional, decreasing, and non linear

Answer 5

Based on the options provided, the most appropriate choice for the relationship described by the points is:

• Non-proportional

Here’s the reasoning:

• Proportional: A proportional relationship would pass through the origin (0,0), which is not the case here since the line intersects the y-axis at (0, 2).
• Non-proportional: This term indicates that the relationship does not pass through the origin, which fits our points where the line crosses the y-axis at (0, 2).
• Decreasing: The relationship is not decreasing since the points show an increase in y as x increases.
• Non-linear: The relationship is linear (not non-linear) since it can be represented by a straight line.

So the correct choice from your options is non-proportional.