Answer:
The value of k is 2.
Step-by-step explanation:
Since, graph of line f of x going through ordered pairs 0, 0 and 2, 4.
So, the equation of line f(x) is,
[tex]y-0=\frac{4-0}{2-0}(x-0)[/tex]
[tex]y=\frac{4}{2}x[/tex]
[tex]y=2x[/tex]
[tex]\implies f(x) = 2x[/tex]
Also, the graph of line g of x going through ordered pairs 0, 2 and 1.5, 5,
So, the equation of line g(x) is,
[tex]y-2=\frac{5-2}{1.5-0}(x-0)[/tex]
[tex]y-2=\frac{3}{1.5}x[/tex]
[tex]y-2=2x[/tex]
[tex]y=y=2x+2[/tex]
[tex]\implies g(x)=2x+2[/tex]
Thus, g(x)=f(x) + k
[tex]\implies 2x+2=2x+k[/tex]
[tex]\implies k = 2[/tex]
Hence, the value of k is 2.
