Question

A line has a slope of 2/3 and contains point A(-6,-4) and point B (a, 2) what is the value of a?

Answer 1

From the point-slope formula, we have:

`y-y_0=m(x-x_0)`

where m is the slope, (x_0,y_0) are known points.

In this case, we have the slope and two points, we can substitute in the formula to get:

`\begin{gathered} \text{if:} \\ (x,y)=(-6,-4) \\ \text{and} \\ (x_0,y_0)=(a,2) \\ \Rightarrow-4-2=(2)/(3)(-6-a) \\ \Rightarrow-6=-(2\cdot6)/(3)-(2)/(3)a \\ \Rightarrow-6=-4-(2)/(3)a \\ \Rightarrow-6+4=-(2)/(3)a \\ \Rightarrow-2=-(2)/(3)a\Rightarrow a=-(2)/(-(2)/(3))=(3\cdot2)/(2)=(6)/(2)=3 \\ a=3 \end{gathered}`

therefore, a=3

Note: you can also find a if you use the slope formula.