Which equation represents the same line as the points in the table?

Question

Input (x)
Output (y)

−3
−6

0
−4

6
0

Responses

A. y=23x−4
y is equal to 2 thirds x minus 4

B. y=−2x+6
y is equal to negative 2 x plus 6

C. y=4x+6
y is equal to 4 x plus 6

D. y=−4x+23

Answer 1

To find the equation for the line passing through the points in the table, we can calculate the slope using the first two points (-3, -6) and (0, -4).

Slope (m) = (y2 - y1) / (x2 - x1)
Slope (m) = (-4 - (-6)) / (0 - (-3))
Slope (m) = (-4 + 6) / (0 + 3)
Slope (m) = 2 / 3

Now that we have the slope, we can use the point-slope form of the equation of a line to find the equation:

y - y1 = m(x - x1)
y - (-6) = 2/3(x - (-3))
y + 6 = 2/3(x + 3)
y + 6 = 2/3x + 2
y = 2/3x - 4

Therefore, the equation that represents the same line as the points in the table is y = 2/3x - 4, which matches option A.