Question

Question 2 - 10 PointsFind the equation of the linear function represented by the table below in slope-intercept form.Answer: y = ???(Important: Please check the attached photo before answering the question)

Answer 1

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

`y=mx+b`

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

`m=(y_2-y_1)/(x_2-x_1)`

Now we need to choose any two points from the given table.

Let's choose the first two points.

`(x_1,y_1)=\mleft(0,-3\mright)\text{ and }(x_2,y_2)=(1,1)`

Let us substitute these values into the slope formula

`m=(1-(-3))/(1-0)=(1+3)/(1)=(4)/(1)=4`

So the slope of the linear function is 4 and the equation becomes

`y=4x+b`

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

`\begin{gathered} -3=4(0)+b \\ -3=0+b \\ b=-3 \end{gathered}`

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

`y=4x-3`