Question

Which of the following equations represents a line that passes through the points (3, 2) and (0,3)

Answer 1

Let's begin by listing out the information given to us:

`\begin{gathered} (x_1,y_1)=(3,2) \\ (x_2,y_2)=\mleft(0,3\mright) \end{gathered}`

We will proceed by calculating the slope:

`\begin{gathered} slope(m)=(\Delta y)/(\Delta x)=(y_2-y_1)/(x_2-x_1)=(3-2)/(0-3)=(1)/(-3)=-(1)/(3) \\ m=-(1)/(3) \end{gathered}`

Next is to use the point-slope formula to find an equation for the line:

`\begin{gathered} \mleft(y-y_1\mright)=m(x-x_1) \\ x_1=3,y_1=2,m=-(1)/(3) \\ y-2=-(1)/(3)(x-3)\Rightarrow y-2=-(1)/(3)x+1 \\ \text{Put like terms together, we have:} \\ y=-(1)/(3)x+1+2\Rightarrow y=-(1)/(3)x+3 \\ y=-(1)/(3)x+3 \end{gathered}`