Question

How do you graph the equation \[3x+y=-1\]?

Answer 1

Hint: In this problem, we are going to graph the equation \[3x+y=-1\], we know that the equation of the line with slope m and making an intercept b on Y-axis, that is the slope-intercept form is \[y=mx+b\]where x and y are coordinates. Here we have to find the x-intercept and y-intercept, to plot the graph. We know that at x-intercept y = 0 and at y-intercept x = 0, from this we have to find x y-intercept and a point on the line to plot the graph.

Complete step by step answer:
We know that the equation of the line with slope m and making an intercept b on the Y-axis is
\[y=mx+b\]……… (1)
We also know that the given line equation is
\[3x+y=-1\]
We can write the above equation in the slope-intercept form
\[y=-3x-1\]…….. (2)
Now we have to find the x-intercept to get the first point.
We know that for x-intercept, y = 0.
Here, we can substitute the value of y in the equation (2), we get
\[\begin{align}
  & \Rightarrow y=-3\left( x \right)-1 \\
 & \Rightarrow 0=-3x-1 \\
 & \Rightarrow x=-\dfrac{1}{3} \\
\end{align}\]
Therefore, x-intercept is at the point \[\left( -\dfrac{1}{3},0 \right)\]……. (3)
Now we have to find y-intercept to get the second point.
We know that for y-intercept, x = 0.
Here we can substitute the value of x in the equation (2), we get
\[\begin{align}
  & \Rightarrow y=-3\left( 0 \right)-1 \\
 & \Rightarrow y=-1 \\
\end{align}\]
Therefore, y-intercept is at the point \[\left( 0,-1 \right)\]……. (4)
Now we can find another point, which lies on the line, we can assume x=-1,
\[\begin{align}
  & \Rightarrow y=-3\left( -1 \right)-1 \\
 & \Rightarrow y=2 \\
\end{align}\]
We found an another point on the line is \[\left( -1,2 \right)\]…… (5)
Now we have three points (3), (4) and (5) to be plotted in the graph.

Note:
Students make mistakes in finding the x-intercept and y-intercept. Students should always remember that at x-intercept the value of y = 0 and at y-intercept the value of x = 0. Students may also make mistakes in plotting the graph, make sure that you are plotting the correct point in the correct axis, and also plot those points in a correct quadrant.