Question

Which is the slope of the line that passes through the points (2,10) and (5,8)?

A. slope = 2/3
B. slope = 7/5
C. Slope = 2/5
D. slope = -2/3

Answer 1

Slope = (Y2 - Y1) / (X2 -X1)

Slope = (8 -10) / (5 -2)

Slope = -2 / 3

Answer is D

Answer 2

D. slope = -2/3

Explanation:

A first order function is given by the following formula:

`y = ax + b`

In which a is the slope.

In this problem, we have that:

The line passes through the point (2,10). This means that when
`x = 2, y = 10`. So

`2a + b = 10`

The line also passes through the point (5,8). This means that when
`x = 5, y = 8`. So

`5a + b = 8`

So we solve a system with these two equations.

I am going to write b as a function of a in the second equation, and replace on the first. So

`b = 8 - 5a`

`2a + b = 10`

`2a + 8 - 5a = 10`

`-3a = 2`

`a = -(2)/(3)`

The correct answer is:

D. slope = -2/3