Question

On a graph there is a positive slope with the following points: (2,5) , (1,3) , (0,1) , (-1,-1) , (-2,-3)
Fill in the blanks.
This is a () relationship. The y-intercept is () and the slope is (). The equation of the line is slope-intercept form is ().
Word Bank for 1st sentence: Proportional or non proportional
Word Bank for 2nd sentence: 2 ,1/2 , (1,0) , (0,1)
Word Bank for 3rd sentence: 2, 1/2 , (1,0) , (0,1)
Word Bank for 4th sentence: y=1x+2 , y=1/2+1 , y=2x+1 , y=1/2x

Answer 1

Let's analyze the points given: (2,5), (1,3), (0,1), (-1,-1), and (-2,-3).

1. **Type of Relationship**: Since the line does not pass through the origin (0,0) and has a y-intercept of (0,1), it represents a **non-proportional** relationship.

2. **Y-Intercept**: The point where the line crosses the y-axis is (0,1), so the y-intercept is **(0,1)**.

3. **Slope**: To find the slope, we can use two points. For instance, using (0,1) and (2,5):
\[
\text{slope} = \frac{y_2 - y_1}{x_2 - x_1} = \frac{5 - 1}{2 - 0} = \frac{4}{2} = 2.
\]
Therefore, the slope is **2**.

4. **Equation of the Line**: Using the slope-intercept form \( y = mx + b \):
\[
y = 2x + 1,
\]
where \( m = 2 \) (slope) and \( b = 1 \) (y-intercept).

Now, we can fill in the blanks accordingly:

This is a **non-proportional** relationship. The y-intercept is **(0,1)** and the slope is **2**. The equation of the line in slope-intercept form is **y=2x+1**.