Answer:
The value of k is 1
Explanation:
Given that a linear function goes through the points (3, 7) a nd (k, 4).
The slope of this line is given as:
[tex]\frac{4-7}{k-3}[/tex]which is the change in y divided by the change in x
The slope is given to be 3/2, therefore, we have:
[tex]\frac{4-7}{k-3}=\frac{3}{2}[/tex]We can solve for k from the above equation
[tex]\begin{gathered} \frac{-3}{k-3}=\frac{3}{2} \\ \\ k-3=-3\times\frac{2}{3} \\ \\ k-3=-2 \\ \text{Add 3 to both sides} \\ \\ k=-2+3 \\ =1 \end{gathered}[/tex]