Answer: The equation of the line is [tex] y=-\dfrac{5}{2}x-1.[/tex]
Step-by-step explanation: We are given to find the equation of the line that is parallel to the line 5x + 2y = 12 and passes through the point (−2, 4).
The slope-intercept form of a straight line is
[tex]y=mx+c,[/tex] where 'm' is the slope of the line and 'c' is the y-intercept.
From the given equation, we have
[tex]5x+2y=12\\\\\Rightarrow 2y=-5x+12\\\\\Rightarrow y=-\dfrac{5}{2}x+6.[/tex]
So, the slope of the line is given by
[tex]m=-\dfrac{5}{2}.[/tex]
We know that the slopes of two parallel lines are equal.
Therefore, the equation of the line parallel to the line 5x + 2y = 12 and passing through the point (-2, 4) is given by
[tex]y-4=m(x-(-2))\\\\\Rightarrow y-4=-\dfrac{5}{2}(x+2)\\\\\Rightarrow 2(y-4)=-5(x+2)\\\\\Rightarrow 2y-8=-5x-10\\\\\Rightarrow 2y=-5x-2\\\\\Rightarrow y=-\dfrac{5}{2}x-1.[/tex]
Thus, the required equation of the line is [tex] y=-\dfrac{5}{2}x-1.[/tex]
