inGiven that the slope,s, is
[tex]s=\frac{change\text{ in y}}{change\text{ in x}}[/tex]
Also given that:
[tex]\begin{gathered} \text{when:} \\ x=-5,y=-16 \\ x=-2,y=-7 \\ x=0,y=-1 \\ x=3,y=8 \\ x=5,y=14 \end{gathered}[/tex]
To find the slope from the given values of x and corresponding values of y
Taking two values of x and y
[tex]\begin{gathered} x=-5,y=-16 \\ x=-2,y=-7 \\ s=\frac{-7--16}{-2--5} \\ s=\frac{-7+16}{-2+5} \\ s=\frac{9}{3} \\ s=3 \end{gathered}[/tex]
[tex]\begin{gathered} x=-2,y=-7 \\ x=0,y=-1 \\ s=\frac{-1--7}{0--2} \\ s=\frac{-1+7}{0+2} \\ s=\frac{6}{2} \\ s=3 \end{gathered}[/tex]
Taking another values of x and y
[tex]\begin{gathered} x=3,y=8 \\ x=5,y=14 \\ s=\frac{14-8}{5-3} \\ s=\frac{6}{2} \\ s=3 \end{gathered}[/tex]
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The slope is the same at the two instances. Hence, the slope is 3
