Question

I couldn’t finish the photo but it’s find the equation of the linear function represented by the table below in the slope- intercept form .

Answer 1

So we have a table of values that belong to a linear function. The slope-intercept form of these type of functions is:

`y=mx+b`

Where m is the slope and b the y-intercept. If we substitute any of the x values in place of x in the equation it will give us the corresponding y values. In order to find m and b we need to take two rows of the table, substitute their x and y values in the equation and consequently build two equations for m and b. Let's take the first two rows. Then we have x=-1 and y=3 in the first equation and x=2 and y=9 in the second:

`\begin{gathered} y=mx+b \\ 3=-m+b\text{ first equation} \\ 9=2m+b\text{ second equation} \end{gathered}`

So now we have to solve these two equations, let's begin with the first one by adding m at both sides of the equal symbol:

`\begin{gathered} 3=-m+b \\ 3+m=-m+m+b \\ 3+m=b \end{gathered}`

So now we have an expression for b that depends on m. The following step is to substitute this in place of m in the first equation:

`\begin{gathered} 9=2m+b \\ 9=2m+(m+3) \\ 9=2m+m+3 \\ 9-3=3m \\ 6=3m \\ m=(6)/(3)=2 \end{gathered}`

So now we know that m=2. If we substitute this value in the expression for b we get:

`\begin{gathered} b=3+m \\ b=3+2=5 \end{gathered}`

So now that we have found the values of m and b we can write the equation of the linear function represented in the table:

`y=2x+5`

Which is the answer to our problem.