Question

Write an equation in the form y = mx + c suggested by the pattern in the table.

Answer 1

y = 2x - 1

Step-by-step explanation

We want to find the equation that represents the data in the table in the form:

y = mx + b

where m = slope

b = y intercept

To do this, we have to first find the slope of the equation using the formula for slope:

`m=(y2-y1)/(x2-x1)`

where (x1, y1) and (x2, y2) are two sets of data points from the table.

Let us pick (0, -1) and (1, 1) as (x1, y1) and (x2, y2) respectively.

Therefore, the slope, m, is:

`\begin{gathered} m=(1-(-1))/(1-0)=(1+1)/(1)=(2)/(1) \\ m=2 \end{gathered}`

Now, we use the point-slope method to find the equation:

`y-y1=m(x-x1)`

Therefore, the equation is:

`\begin{gathered} y-(-1)=2(x-0) \\ y+1=2(x) \\ y+1=2x \\ y=2x-1 \end{gathered}`

That is the equation.