Question

a line has a slope of 9/5 if one of the points on the line is (-10, -16), which of the following could be another point on the line?​

Answer 1

(0,2) is the answer - Option C.

Explanation:

Equation of a line:

The equation of a line, in point-slope form, is given by:

`y - y_0 = m(x - x_0)`

In which m is the slope and the point is
`(x_0,y_0)`

Slope of 9/5 if one of the points on the line is (-10, -16)

This means that
`m = (9)/(5), (x_0,y_0) = (-10,-16)`. So

`y - y_0 = m(x - x_0)`

`y - (-16) = (9)/(5)(x - (-10))`

`y + 16 = (9)/(5)(x + 10)`

Which of the following could be another point on the line?​

We have to find a point for values of x and y which gives us an identity. So

Option A:

x = -5, y = -6

Lets see

`-6 + 16 = (9)/(5)(-5+10)`

`10 = (9*5)/(5)`

`10 = 9` -> False

So this is not the answer.

Option B:

x = 4, y = 11

`11 + 16 = (9)/(5)(4 + 10)`

`27 = 9*14/5`

False

Option C:

x = 0, y = 2

`2 + 16 = (9)/(5)(x+10)`

`(90)/(5) = 18`

`18 = 18`

True, so (0,2) is the answer - Option C.