Answer: The required equation of the line is [tex]2x-5y+24=0.[/tex]
Step-by-step explanation: We are given to find the equation that represents a line passing through the point (-2, 4) and has a slope of [tex]\dfrac{2}{5}.[/tex]
We know that
the equation of a straight line passing through the point (a, b) and having slope m is given by
[tex]y-b=m(x-a).[/tex]
For the given line, we have
[tex]m=\dfrac{2}{5},~~~(a,b) = (-2,4).[/tex]
Therefore, the equation of the line is given by
[tex]y-4=\dfrac{2}{5}(x-(-2))\\\\\\\Rightarrow 5(y-4)=2(x+2)\\\\\Rightarrow 5y-20=2x+4\\\\\Rightarrow 2x-5y+24=0[/tex]
Thus, the required equation of the line is [tex]2x-5y+24=0.[/tex]
