Question

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

Answer 1

Options (A) and (C)

Explanation:

From table attached,

Let the equation of a linear equation that represents the input-output values in the table is,

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

Where (x', y') is a point lying on the graph.

And m = slope of the line passing through two points
`(x_1,y_1)` and
`(x_2,y_2)`

m =
`(y_2-y_1)/(x_2-x_1)`

Slope of the line passing through (0, 11) and (1, 5) will be,

m =
`(11-5)/(0-1)`

m = -6

Therefore, equation of the line passing through (0, 11) and slope = -6 will be,

y - 11 = -6(x - 0)

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

y - 5 = -6(x - 1)

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

y + 1 = -6(x - 2)

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

y + 7 = -6(x - 3)

Therefore, Options (A) and (C) are the correct options.