Question

Answer the questions from the graph. (4 points) 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.

here are the pin points I gathered
-4, 0 / -2, 1 / 0, 2 / 2, 3

Answer 1

linear could also mean proportional yeah?

Answer 2

To analyze the points you've provided and answer the questions:

1. **Identifying the y-intercept**: The y-intercept is the value of y when x = 0. From your points, the coordinate (0, 2) indicates that the y-intercept is 2.

**Y-intercept**: 2

2. **Calculating the slope**: The slope (m) is calculated by taking the change in y (Δy) and dividing it by the change in x (Δx). Using two points, for example (-2, 1) and (0, 2):

- Δy = y2 - y1 = 2 - 1 = 1
- Δx = x2 - x1 = 0 - (-2) = 2

Now, calculate the slope:
\[
m = \frac{Δy}{Δx} = \frac{1}{2}
\]

**Slope**: \(\frac{1}{2}\)

3. **Finding the equation of the line in slope-intercept form (y = mx + b)**: The slope-intercept form is represented as \(y = mx + b\), where m is the slope and b is the y-intercept.

Using the slope (m = \(\frac{1}{2}\)) and the y-intercept (b = 2):
\[
y = \frac{1}{2}x + 2
\]

**Equation of the line**: \(y = \frac{1}{2}x + 2\)

4. **Type of relationship**: The relationship represented by the line is linear because it forms a straight line on the graph.

**This is a**: linear relationship

Here is a summary of the responses:

- Y-intercept: 2
- Slope: \(\frac{1}{2}\)
- Equation of the line: \(y = \frac{1}{2}x + 2\)
- Type of relationship: linear relationship

Answer 3

Yes, you are correct! In mathematical terms, a linear relationship can indeed be either proportional or non-proportional.

1. **Proportional Relationship**: A relationship is proportional if it can be expressed in the form \(y = kx\), where \(k\) is a constant. In this case, the line passes through the origin (0, 0). An example of a proportional linear relationship would be \(y = 2x\).

2. **Non-Proportional Linear Relationship**: A linear relationship is non-proportional if it can be expressed in the form \(y = mx + b\), where \(b\) (the y-intercept) is not equal to 0. Your example \(y = \frac{1}{2}x + 2\) is a non-proportional linear relationship since the y-intercept (b) is 2, meaning that the line does not pass through the origin.

Given that the y-intercept in your example is not zero, the relationship described by the equation \(y = \frac{1}{2}x + 2\) is a non-proportional linear relationship.

So, while all proportional relationships are linear, not all linear relationships are proportional.