Question

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

Answer 1

Answer:

D. slope = -2/3

Step-by-step 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

$b = 8 - 5a$

$2a + b = 10$

$2a + 8 - 5a = 10$

$-3a = 2$

$a = -\frac{2}{3}$

The correct answer is:

D. slope = -2/3

Answer 2

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

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

Slope = -2 / 3

Answer is D