Question

Graph the line with a slope of 3 that passes through (4,1)

Answer 1

Given that the slope is m=3 and that the line passes through the point (4,1), we can use the point-slope formula to find the equation of the line:

`\begin{gathered} (x_1,y_1)=(4,1) \\ m=3 \\ y-y_1=m(x-x_1) \\ \Rightarrow y-1=3(x-4)=3x-12 \\ \Rightarrow y=3x-12+1=3x-11 \\ y=3x-11 \end{gathered}`

Now we can easily graph the line if we make y=0 and x=5

`\begin{gathered} if\colon x=5 \\ \Rightarrow y=3\cdot5-11=15-11=4 \\ y=-11 \\ if\colon y=0 \\ \Rightarrow0=3x-11 \\ \Rightarrow3x=11 \\ \Rightarrow x=(11)/(3) \end{gathered}`

Then the graph is the following: