Parallel lines have the same slope
The equation of the line is: [tex]y = 2x+5[/tex]
The equation is given as:
[tex]4x - 2y =8[/tex]
Divide through by 2
[tex]2x - y =4[/tex]
Make y the subject
[tex]y = 2x - 4[/tex]
Because the required equation and [tex]y = 2x - 4[/tex] are parallel, then they must have the same slope
A linear equation is represented as:
[tex]y = mx + c[/tex]
Where:
[tex]m = slope[/tex]
So, by comparison
[tex]m = 2[/tex]
This means that the slope of the required line is 2
The equation is then calculated as:
[tex]y = m(x - x_1) + y_1[/tex]
So, we have:
[tex]y = 2(x--2) + 1[/tex]
[tex]y = 2(x+2) + 1[/tex]
Open brackets
[tex]y = 2x+4 + 1[/tex]
[tex]y = 2x+5[/tex]
Hence, the equation of the line is: [tex]y = 2x+5[/tex]
Read more about equations of parallel lines at:
https://brainly.com/question/402319
