Question

A line passes through point (-2, 5) and has a slope of . Points A(x, 3) and B(-2, y) lie on the line.

The value of x is
, and the value of y is
.

Answer 1

The question is incomplete. The complete question is here.

A line passes through point (-2, 5) and has a slope of 2/3. Points A(x, 3) and B(-2, y) lie on the line.

The value of x is ___, the value of y is ___.

Answer:

The value of x is -5, and the value of y is 5

Explanation:

The form of a linear equation is y = m x + b, where

• m is the slope of the line
• b is the y-intercept (value y at x = 0), to find b substitute x and y in the equation by the coordinates of a point on the line

∵ The slope of the line is
`(2)/(3)`

∴ m =
`(2)/(3)`

∵ The form of the equation is y = m x + b

∴ y =
`(2)/(3)` x + b

- Substitute x and y by the coordinates of a point on the line

∵ The line passes through point (-2 , 5)

∴ x = -2 and y = 5

∵ 5 =
`(2)/(3)` (-2) + b

∴ 5 =
`(-4)/(3)` + b

- Add
`(-4)/(3)` to both sides

∴
`(19)/(3)` = b

∴ y =
`(2)/(3)` x +
`(19)/(3)`

∵ Point A (x , 3) lies on the line

- Substitute y by 3 to find x

∴ 3 =
`(2)/(3)` x +
`(19)/(3)`

- Subtract
`(19)/(3)` from both sides

∴
`(-10)/(3)` =
`(2)/(3)` x

- Divide both sides by
`(2)/(3)`

∴ -5 = x

∴ The value of x = -5

∵ Point B (-2 , y) lies on the line

- Substitute x by -2 to find y

∴ y =
`(2)/(3)` (-2) +
`(19)/(3)`

∴ y =
`(-4)/(3)` +
`(19)/(3)`

∴ y =
`(15)/(3)`

∴ y = 5

∴ The value of y = 5