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?

$slope=\frac{1}{3}$

Based on the given conditions formulae

$m=\frac{1}{3},at\text{ points \lparen-3 , 2\rparen}$

Substitute the values in the equation of a line

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

Also substitute ths values into

$\begin{gathered} m=\frac{1}{3},b=3 \\ y=mx+b \\ y=\frac{1}{3}x+3 \end{gathered}$

Using the options that obey the line

$(6,5)\text{ is true}$$\begin{gathered} y=\frac{1}{3}x+3 \\ when\text{ x = 6 , y = 5} \\ y=\frac{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