Question

17. Find the missing value of the line passing through the points (1, 2) and(x, 6) with a rate of change of 2?

Answer 1

The y-intercept form is

`\begin{gathered} y=mx+b \\ \text{where} \\ m\text{ is the slope or the rate of change and} \\ b\text{ is the y-intercept.} \\ \\ \text{Given:} \\ (1,2) \\ (x,6) \\ m=2 \\ \\ \text{Substitute point }(1,2)\text{ and }m\text{ and we have} \\ y=mx+b \\ 2=(2)(1)+b \\ 2=2+b \\ 2-2=b \\ 0=b \\ b=0 \\ \\ \text{The general equation is now} \\ y=2x+0 \\ y=2x \\ \\ \text{Equate }y=6\text{ to solve for }x \\ y=2x \\ 6=2x \\ (6)/(2)=(2x)/(2) \\ 3=x \\ x=3 \end{gathered}`

Therefore, the missing value x is equal to 3.