Question

Write the equation of this function in the form y=x+b X 0 4 12 у 6 10 18

Answer 1

Step1: Pick 2 points in the table:

(0,6) and (4,10)

Step2: Recall the formula for the slope of a line.

`\text{Slope =}(y_2-y_1)/(x_2-x_1)`

Step3: Substitute the values of the coordinates in the above formula.

`\begin{gathered} (0,6)\Rightarrow x_1=0;y_1=6 \\ (4,10)\Rightarrow x_2=4;y_2=10 \end{gathered}`

Step4:

`\text{Slope =}(10-6)/(4-0)=(4)/(4)=1`

Step5: Invoke the formula for the equation of the line.

`\begin{gathered} y-y_1=slope(x-x_1) \\ y-6=1(x-0) \\ y-6=x \\ y=x+6 \end{gathered}`

Hence, the correct answer is y = x + 6