We are given a table of x and y values.
We are asked to find the equation of the linear function in the slope-intercept form.
The equation of the linear function in slope-intercept form is given by
[tex]y=mx+b[/tex]
Where m is the slope and b is the y-intercept.
So our goal is to find these two values (slope and y-intercept)
The slope (m) is given by
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
Now we need to choose any two points from the given table.
Let's choose the first two points.
[tex](x_1,y_1)=\mleft(0,-3\mright)\text{ and }(x_2,y_2)=(1,1)[/tex]
Let us substitute these values into the slope formula
[tex]m=\frac{1-(-3)}{1-0}=\frac{1+3}{1}=\frac{4}{1}=4[/tex]
So the slope of the linear function is 4 and the equation becomes
[tex]y=4x+b[/tex]
Now we need to find the y-intercept (b)
Choose any one point from the table
Let choose (0, -3) and substitute it into the above equation
[tex]\begin{gathered} -3=4(0)+b \\ -3=0+b \\ b=-3 \end{gathered}[/tex]
Please note that even if you had chosen any other point then still you would have gotten the same y-intercept.
Therefore, the equation of the linear function in slope-intercept form is
[tex]y=4x-3[/tex]
