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Question 2 Multiple Choice Worth 4 points)
(05.02)
Two quantities are related, as shown in the table:
X Y
2 3
4 4
6 5
8 6
Which equation best represents the relationship?
Oy = x + 2
Oy = x + 1
Oy = x + 2
Oy = 2x + 1

Question 2 Multiple Choice Worth 4 points 0502 Two quantities are related as shown in the table X Y 2 3 4 4 6 5 8 6 Which equation best represents the relations class=

Respuesta :

Option A : [tex]y=\frac{1}{2}x+2[/tex] is the equation that best represents the relationship

Explanation:

From the given table, the coordinates of the two quantities are [tex](2,3)[/tex], [tex](4,4)[/tex] , [tex](6,5)[/tex] and [tex](8,6)[/tex]

We need to determine the equation that best represent the relationship.

The equation can be determined by substituting the values in the slope - point formula,

[tex]y-y_1=m(x-x_1)[/tex]

First, we shall determine the slope.

Let us consider the coordinates [tex](2,3)[/tex] and [tex](6,5)[/tex]

The formula to find the slope is given by

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

Substituting these coordinates, we get,

[tex]m=\frac{5-3}{6-2}[/tex]

[tex]m=\frac{2}{4}[/tex]

[tex]m=\frac{1}{2}[/tex]

Thus, the slope is [tex]m=\frac{1}{2}[/tex]

Now, we shall substitute any one of the coordinates and the slope in the formula [tex]y-y_1=m(x-x_1)[/tex]

Let us substitute the coordinate [tex](4,4)[/tex] and [tex]m=\frac{1}{2}[/tex], we get,

[tex]y-4=\frac{1}{2}(x-4)[/tex]

[tex]y-4=\frac{1}{2}x-2[/tex]

     [tex]y=\frac{1}{2}x+2[/tex]

Thus, the equation that best represents the relationship is [tex]y=\frac{1}{2}x+2[/tex]

Hence, Option A is the correct answer.

akposevictor

The linear equation, in slope-intercept form, that best represents the relationship is: A. y = 1/2x + 2.

Linear equation in Slope-intercept Form

  • The equation of a relation, in slope-intercept form, is represented as: y = mx + b.
  • m = slope; b = y-intercept.
  • Slope = change in y/change in x.

First, find the slope (m) using, (2, 3) and (6, 5):

Slope (m) = (5 - 3)/(6 - 2)

Slope (m) = 1/2

Find "b" by substituting (x, y) = (2, 3) and m = 1/2 into y = mx + b.

Thus:

3 = 1/2(2) + b

3 = 1 + b

3 - 1 = b

b = 2

Substitute b = 2 and m = 1/2 into y = mx + b:

y = 1/2x + 2

Therefore, the linear equation, in slope-intercept form, that best represents the relationship is: A. y = 1/2x + 2.

Learn more about slope-intercept form on:

https://brainly.com/question/1884491

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