Question

This table represents a linear relationship between x and y.

X Y
-6 -3
-4 -2
-2 -1
0 0
Based on the linear relationship in
this table, what is the value of y when x is 4?

A. 1
B. 2
C. 3
D. 4

Answer 1

y = 2

Explanation:

Given table:

`\underline{\ \ \ \ \ \ \ \ \ \ \ \ \ \ } \\\underline{| \ \ \text{x} \ \ | \ \ \text{y} \ \ | } \\ \underline{| \ \text{-6} \ \ | \ \text{-3} \ \ |} \\ | \underline{\ \text{-4} \ \ | \ \text{-2} \ \ | }\\ \underline{| \ \text{-2} \ \ | \ \text{-1} \ \ |} \\ \underline{| \ \ \text{0} \ \ | \ \ 0 \ \ |}`

To determine the value of y when "x" is 4, we need to determine the equation of the line that represents the table given. Then, we can substitute the value of "x" in the equation to determine the value of y.

Determining the equation of the line that represents the table:

Y-intercept:

Since the coordinate (0, 0) is included in the table, we can tell that the equation of the line that represents the table passes through the origin. Therefore, we can tell that the y-intercept is 0 as the y-intercept is the point on the line that intersects the y-axis.

Slope:

The slope of the line can be determined by picking any two points in the table and substituting the coordinates of the chosen points in the slope formula. Let our chosen points be (-6, -3) and (0, 0).

`\implies \text{Slope} = (y_(2) - y_(1) )/(x_(2) - x_(1) )`

`\implies \text{Slope} = (0 - (-3) )/(0 - (-6) )`

`\implies \text{Slope} = (0 + 3 )/(0 + 6 )`

`\implies \text{Slope} = (3)/(6) = (1)/(2)`

Equation of line:

The equation of the line represented by the table in slope intercept form is y = mx + b, where "m" is the slope and "b" is the y-intercept.

Obtained slope and y-intercept:

• Slope = 1/2
• y-intercept = 0

⇒ y = (1/2)x + 0

⇒ y = x/2

Therefore, the equation of the line is y = x/2.

Determining the value of y when "x" is 4:

Obtained equation of line that represents the table:

• ⇒ y = x/2

Given value:

• x = 4

Therefore,

• ⇒ y = (4)/2
• ⇒ y = 2

Thus, the value of "y" when "x" is 4 is 2.