Question

If the points (2,3) and (5,y) lie on a line whose slope is -7/6, what does y equal?

Answer 1

`y=-(1)/(2)=-0.5`

Explanation:

Given points :

(2,3) and (5,y)

Slope of line =
`-(7)/(6)`

To find the value of
`y`.

We will apply the slope formula to find slope using the given points.

Slope
`m` of a line with points
`(x_1,y_1)` and
`(x_2,y_2)` is given by:

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

Plunging in the given points (2,3) and (5,y) in the formula.

`m=(y-3)/(5-2)`

`m=(y-3)/(3)`

We know the slope of line =
`-(7)/(6)`

So, we will equate and solve for
`y`

`(y-3)/(3)=-(7)/(6)`

Multiplying both sides by 6 to remove fractions.

`6* (y-3)/(3)=6*-(7)/(6)`

`2(y-3)=-7`

Using distribution.

`2y-6=-7`

adding 6 both sides.

`2y-6+6=-7+6`

`2y=-1`

Dividing both sides by 2.

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

∴
`y=-(1)/(2)=-0.5` (Answer)