Question

The points (8,
-
4) and (10,n) fall on a line with a slope of 4. What is the value of n?

Answer 1

n = 4

calculate the slope m using the gradient formula

m = (y₂ - y₁ ) / (x₂ - x₁ )

with (x₁, y₁ ) = (8, - 4 ) and (x₂, y₂ ) = (10, n )

m =
`(n+4)/(10-8)` =
`(n+4)/(2)`

now m = 4, hence

`(n+4)/(2)` = 4 ( multiply both sides by 2 )

n + 4 = 8 ( subtract 4 from both sides )

n = 4

Answer 2

If a slope of the line is 4, then the equation of the line is

y=4x+b.

This line passes through the point (8,-4), this means that coordinates of this point satisfy the equation:

-4=4·8+b,

b=-4-32,

b=-36.

Thus, the equation of the line is y=4x-36.

Now, substitute the coordinates of the point (10,n) into the equation:

n=4·10-36,

n=40-36,

n=4.

Answer: n=4.