Question

Identify the slope and the y-intercept of each line and use them to write an equation of the graph

Answer 1

Notice that the line passes through the point (0,1) and the point (3,-1). Then, we have the following:

`\begin{gathered} y-\text{intercept: (0,1)} \\ \text{slope:} \\ m=(y_2-y_1)/(x_2-x_1) \\ \Rightarrow m=(-1-0)/(3-0)=-(1)/(3) \\ m=-(1)/(3) \end{gathered}`

now we can find the equation of the line using the slope and the y-intercept:

`\begin{gathered} y-y_1=m(x-x_1) \\ \Rightarrow y-1=-(1)/(3)(x-0) \\ \Rightarrow y=-(1)/(3)x+1 \end{gathered}`

therefore, the equation of the line is y=-1/3x+1