On a graph there is a positive slope with the following points: (2,5) , (1,3) , (0,1) , (-1,-1) , (-2,-3)

Question

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.