Question

C) (3 ,5) and (k , 9), slope = 1/2 what is the value of k ? help please I don't know what to do

Answer 1

You know that a determined line has a slope m=1/2 and crosses the points (3, 5) and (k, 9)

You need to determine the value of k.

First step is to determine the equation of the line. For this, use the point-slope form

`y-y_1=m(x-x_1)`

Where

(x₁, y₁) are the coordinates of a point on the line

Using (3, 5) and m=1/2

`\begin{gathered} y-5=(1)/(2)(x-3) \\ y-5=(1)/(2)x-3\cdot(1)/(2) \\ y-5=(1)/(2)x-(3)/(2) \\ y=(1)/(2)x-(3)/(2)+2 \\ y=(1)/(2)x+(7)/(2) \end{gathered}`

Now that we know the equation of the line, you can calculate the value of k

For the point (k, 9)

The x-coordinate is k

The y-coordinate is 9

`\begin{gathered} 9=(1)/(2)k+(7)/(2) \\ 9-(7)/(2)=(1)/(2)k \\ (11)/(2)=(1)/(2)k \\ k=11 \end{gathered}`

The value of k is 11