Question

In a diagram, the lines y = bx - 9 and 3x + 2y = 15 intersect at the point (k, k). What is the value of b?

Answer 1

`b=4`

Step-by-step explanation

The two lines given are:

`\begin{gathered} y=bx-9 \\ 3x+2y=15 \end{gathered}`

They intersect at the point (k, k). This means that at that point, they have the same values of x and y.

First, find the value of k by substituting (k, k) for (x, y) in the second equation:

`\begin{gathered} 3(k)+2(k)=15 \\ 3k+2k=15 \\ 5k=15 \\ \Rightarrow k=(15)/(5) \\ k=3 \end{gathered}`

Therefore, the point they intersect is (3, 3).

To find the value of b, substitute (3, 3) for (x, y) in the first equation and simplify:

`\begin{gathered} 3=b(3)-9 \\ 3=3b-9_{} \\ \Rightarrow3b=3+9=12 \\ \Rightarrow b=(12)/(3) \\ b=4 \end{gathered}`

That is the value of b.