Answer:
y = 0.5x + 5
Explanation:
The equation of a line can be calculated as:
[tex]y=m(x-x_1)+y_1[/tex]Where m is the slope and (x1, y1) is a point in the line.
To find the slope of our line, we need to identify the slope of the given line.
Since the equation of the given line is y = -2x + 1, the slope of this line is -2, because it is the number beside the x.
Then, two lines are perpendicular if the product of their slopes is equal to -1. So, we can write the following equation:
[tex]-2\cdot m=-1[/tex]Therefore, the slope m of our line will be:
[tex]m=\frac{-1}{-2}=0.5[/tex]Now, we can replace the value f m by 0.5 and the point (x1, y1) by (0, 5) and we get that the equation of the line is:
[tex]\begin{gathered} y=0.5(x-0)+5 \\ y=0.5(x)+5 \\ y=0.5x+5 \end{gathered}[/tex]Therefore, the answer is y = 0.5x + 5
