Question

how do i find the slope of this with change in y/change in x if this table isn't changing by the same amount each time

Answer 1

inGiven that the slope,s, is

`s=\frac{change\text{ in y}}{change\text{ in x}}`

Also given that:

`\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}`

To find the slope from the given values of x and corresponding values of y

Taking two values of x and y

`\begin{gathered} x=-5,y=-16 \\ x=-2,y=-7 \\ s=(-7--16)/(-2--5) \\ s=(-7+16)/(-2+5) \\ s=(9)/(3) \\ s=3 \end{gathered}`

`\begin{gathered} x=-2,y=-7 \\ x=0,y=-1 \\ s=(-1--7)/(0--2) \\ s=(-1+7)/(0+2) \\ s=(6)/(2) \\ s=3 \end{gathered}`

Taking another values of x and y

`\begin{gathered} x=3,y=8 \\ x=5,y=14 \\ s=(14-8)/(5-3) \\ s=(6)/(2) \\ s=3 \end{gathered}`

The slope is the same at the two instances. Hence, the slope is 3