Question

A line has a slope of 1/3 and includes the points (6,1) and (9,j). What is the value of j?

Answer 1

j = 2

Explanation:

Slope of a line is given by:

`\medium \text{$(y_(2)-y_(1))/(x_(2)-x_(1))$}`

where (x₁, y₁) and (x₂, y₂) are two points on the line

This is commonly referred to as rise/run

Given the two points (6, 1) corresponding to (x₁, y₁) and (9, j) corresponding to (x₂, y₂)

`\text{Slope = }\frac{\ensuremath{j}-1}{9-6}=(j-1)/(3)`

But we are given the slope as 1/3

So we get

`(j-1)/(3) = (1)/(3)`

Multiplying by 2 on both sides gives us:

j - 1 = 1

Adding 1 to both sides gives us

j - 1 + 1 = 1 + 1

j = 2