Question

Use graph of $y=3x-1$. For each ordered pair, decide :

(a) Is the ordered pair $A(3,-1)B(-1,-4)$a solution to the equation.

(b) Is the point $A(3,-1)B(-1,-4)$on the line?

Short answer

The ordered pair $A(3,-1)$is not a solution to the equation and $B(-1,-4)$is a solution to the equation and similarly the point $A(3,-1)$ does not lie on the line and point$B(-1,-4)$lies on the line.

Step-by-step solution

Given Information

We are given the points$A(3,-1)B(-1,-4)$and equation of line$y=3x-1$

Part(a) Step 1: Calculation

Substitute the coordinates $x=3,y=-1$in the given equation of line to check whether the ordered pair is a solution or not.

role="math" localid="1644335330701" $$\begin{gathered} y=3x-1 \\ -1\stackrel{?}{=}3\left(3\right)-1 \\ -1\stackrel{?}{=}9-1 \\ -1\ne 8 \end{gathered}$$

Next, substitute the coordinates $x=-1,y=-4$in the given equation of line to check whether the ordered pair is a solution or not.

$$\begin{gathered} y=3x-1 \\ -4\stackrel{?}{=}3(-1)-1 \\ -4\stackrel{?}{=}-3-1 \\ -4\ne -4 \end{gathered}$$

Part(b) Step 1: Explanation

As we can see that the first point is not the solution to the given equation of line implies that the ordered pair does not lie on the line in the graph and the second point is the solution to the given equation of line implies that the ordered pair lies on the line in the graph.