Answer: We have to find if the ordered pairs are linear or non-linear.
[tex](-1,5)\text{ (-2,2) (-3,0)}[/tex]
Linear equations are of the form:
[tex]y(x)=mx+b[/tex]
where:
[tex]\begin{gathered} m=\frac{\Delta y}{\Delta x} \\ b=y-\text{intercept} \end{gathered}[/tex]
If we plot these three coordinate points, we get the following.
According to this graph, the points do seem to be on the same line:
Confirmation through the equation of the line:
[tex]\begin{gathered} y(x)=mx+b \\ \therefore\rightarrow \\ m=\frac{\Delta y}{\Delta x}=\frac{2-0}{-2--3}=2 \\ \\ \rightarrow \\ 0=2(-3)+b\rightarrow b=6 \\ \therefore\rightarrow \\ y(x)=2x+6 \end{gathered}[/tex]
Plotting the equation on the same graph:
Therefore, we can conclude that these three points are not-linear because only two points lie on the same line.
Confirmation through algebraic approach would be as follows:
• Find slope and y-intercept from any two points
• And, confirm the resultant equation with the three coordinate points
The above steps will ensure the answer.
