What is the equation of the line that passes through the point of intersection of the lines y = 2x − 5 and y = −x + 1, and is also parallel to the line y equals start fraction one over two end fraction x plus four question mark?

Answer:[tex]y = \frac{1}{2}x - 2[/tex]Step-by-step explanation:Given lines,y = 2x - 5,y = -x + 1Subtracting these two equations,0 = 3x - 6[tex]\implies 3x = 6[/tex][tex]\implies x = \frac{6}{3}=2[/tex]By first equation,[tex]y=2(2) -5=4-5 = -1[/tex]Thus, point of intersecting would be (2, -1).Now, the equation of a line is y = mx + c,Where,m = slope of the line,So, the slope of the line [tex]y=\frac{1}{2}x+4[/tex] is 1/2.∵ two parallel lines have same slope.Hence,Equation of the parallel line passes through (2, -1),[tex]y+1=\frac{1}{2}(x-2)[/tex][tex]y+1=\frac{1}{2}x - 1[/tex][tex]y = \frac{1}{2}x - 2[/tex]