Question

I really need help anyone know which option is correct.?

Answer 1

B,
`-(1)/(2)`

Explanation:

This problem is essentially asking one to envision a line passing through the set of points on the coordinate plane, then to find the constant of proportionality of that line. The constant of proportionally, also known as the rate of change, or the slope, is a number that can be used to describe the range that happens between points on a line. The following formula can be used to find the slope of a line passing through a set of points.

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

Where the points (
`x_1,y_1`) and (
`x_2,y_2`) are points on the line.

As one can see, on the given coordinate plane, the points (
`2,-1`), and (
`4,-2`) are on the coordinate plane. Substitute these points into the formula to find the slope of the line, then simplify to evaluate the equation and find the slope,

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

(
`2,-1`), (
`4,-2`)

`=(-2-(-1))/((4)-(2))`

`=(-2+1)/(4-2)\\\\=(-1)/(2)\\\\=-(1)/(2)`