Use the table of points to answer the following questions.

x y
−6 5
−4 4
1 3 over 2

Part A: What is the slope from (−6, 5) to (−4, 4)? Show every step of your work. (1 point)

Part B: What is the slope from (−4, 4) to 1, three halves? Show every step of your work. (1 point)

Part C: What do the slopes from Parts A and B tell you about the relationship between all the points in the table? (2 points)

As both of the slope in part A and B are negative, it tells us that the line is going in downward direction, thus all the points are in a straight line and the relation between all points is linear.

Step-by-step work:

Part A:

The slope from (-6,5) to (-4,4) can be calculated by using the formula:

slope = (y2 - y1) / (x2 - x1)

where (x1, y1) = (-6, 5) and (x2, y2) = (-4, 4)

Therefore, the slope = (4 - 5) / (-4 - (-6)) = (-1) / (-2) = 1/2.

Part B:

The slope from (-4, 4) to (1, 3/2) can be calculated by using the formula:

slope = (y2 - y1) / (x2 - x1)

where (x1, y1) = (-4, 4) and (x2, y2) = (1, 3/2)

Therefore, the slope = (3/2 - 4) / (1 - (-4)) = (-5/2) / 5 = -5/10 = -1/2.

Part C:

The slopes from Part A and B tell us that the points in the table are part of a straight line.

As we know that two points determine a line, slope helps in determining the direction of the line.

A positive slope indicates that the line is going in an upward direction, where a negative slope indicates the line is going in a downward direction.

As both of the slope in part A and B are negative, it tells us that the line is going in downward direction, thus all the points are in a straight line and the relation between all points is linear.

mhanifa mhanifa · Answer 2 · 2023-01-11T06:09:40+01:00

Use the slope equation to find it:

[tex]m=\cfrac{y_2-y_1}{x_2-x_1}[/tex]

Here (x₁, y₁) is the first point and (x₂, y₂) is the second point.

Part A

Find the slope from (−6, 5) to (−4, 4):

[tex]m=\cfrac{4-5}{-4-(-6)} =-\cfrac{1}{2}[/tex]

Part B

Find the slope from (−4, 4) to (1, 3/2):

[tex]m=\cfrac{3/2-4}{1-(-4)} =\cfrac{3/2-8/2}{5}=\cfrac{-5/2}{5}= -\cfrac{1}{2}[/tex]

Part C

The slopes are equal, it means the table represents the same line.