Question

Which of the following equations could represent the points in the table? Select all that apply.

Answer 1

Options (A) and (C)

Explanation:

Let the equation represented by the table is,

y - y' = m(x - x')

where m = slope of the line

(x', y') are the coordinates of a point passing through the line.

Since, slope of the line 'm' =
`(y_2-y_1)/(x_2-x_1)`

Let the two points given in the table are (0, 11) and (1, 5)

Therefore, slope 'm' =
`(11-5)/(0-1)` = -6

Now equation of the line passing through (0, 11) will be,

y - 11 = -6(x - 0)

Equation of the line passing through (1, 5) and slope (-6) will be,

y - 5 = -6(x - 1)

Equation of the line passing through (2, -1) and slope (-6) will be,

y + 1 = -6(x - 2)

Equation of the line passing through (3, -7) and slope (-6) will be,

y + 7 = -6(x - 3)

Therefore, equations given in Options (A) and (C) will be the answer.