That is all the question says. we are working with slope intercept form and standard form and the lessons like that. I just dont get this

## if points are (4,a) and (8,3a) and the slope is 1/3 what is a?

# 2 Answers

Use the slope formula: m = (y2 - y1)/(x2 - x1). In this case:

x1 = 4, y1 = a, x2 = 8, y2 = 3a

so plug in:

m = (3a - a)/(8 - 4) = 2a / 4

But since 2a/4 = 1/3, cross-multiply and solve the proportion. You get

6a = 4, so

a = 4/6 = 2/3

You are given two points on a line:

point 1 ==> **(x**_{1}**, y**_{1}**)**
**=** **(4, a)** ==> where **x**_{1}** = 4** and
**y**_{1}** = a**

point 2 ==> **(x**_{2}**, y**_{2}**)**
**=** **(8, 3a)** ==> where **x**_{2}** = 8** and
**y**_{2}** = 3a **

You are also given that the slope (m) of this line that passes thru these points is 1/3. That is, **m = 1/3**.

Recall that the formula for the slope of a line that passes through any two points (x_{1}, y_{1}) and (x_{2}, y_{2}) is:

** m = (y**_{2}** - y**_{1}**) / (x**_{2}** - x**_{1}**) **

Thus, for the slope of the line that passes through the two points given above we find that:

** 1/3 = (3a - a) / (8 - 4)**

1/3 = (2a) / (4)

**1/3 = a/2**

Multiplying both sides of the equation by 2, we solve for a:

1/3 = a/2

2*(1/3) = 2*(a/2)

** 2/3 = a **