Answer:
k=5
Step-by-step explanation:
Let's find the equation for both lines. For the line in blue we know that passes through points (0,-2) and (3,-1) with this information we can use the formula of the line:
[tex]y-y_1=\frac{y_2-y_1}{x_2-x_1} (x-x_1)[/tex]
so making the susbtitution we get:
[tex]y-(-2)=\frac{-1-(-2)}{3-0}(x-0)[/tex]
[tex]y=\frac{1}{3}x-2[/tex]
For the red line we know that passes through points (0,3) and (3,4) doing the same steps as above we get that
[tex]y-(3)=\frac{4-3}{3-0}(x-0)[/tex]
[tex]y=\frac{1}{3}x+3[/tex]
the value of k is 5 that's why because we need to move 5 units along the y axis to reach the 3 in the red line
