Question

A line passes through the point (-3, 2) and has a slope of 1/3. Which of the following points also lies on this line?

Answer 1

SOLUTIONS

Which of the following points also lies on this line?

`slope=(1)/(3)`

Based on the given conditions formulae

`m=(1)/(3),at\text{ points \lparen-3 , 2\rparen}`

Substitute the values in the equation of a line

`\begin{gathered} y=mx+b \\ (-3,2) \\ 2=(1)/(3)(-3)+b \\ 2=-1+b \\ 2+1=b \\ b=3 \end{gathered}`

Also substitute ths values into

`\begin{gathered} m=(1)/(3),b=3 \\ y=mx+b \\ y=(1)/(3)x+3 \end{gathered}`

Using the options that obey the line

`(6,5)\text{ is true}`
`\begin{gathered} y=(1)/(3)x+3 \\ when\text{ x = 6 , y = 5} \\ y=(1)/(3)(6)+3 \\ y=2+3 \\ y=5 \end{gathered}`

Therefore the only points that lie on the line J (6, 5)

Correct answer = Option D