the equation of the line that is perpendicular to the line with equation y=-2x-1 and passes through the point (1, -2) is?

Linear equations are typically organized in slope-intercept form: [tex]y=mx+b[/tex] where m is the slope and b is the y-intercept (the value of y when the line crosses the y-axis)
Perpendicular lines always have slopes that are negative reciprocals of each other (ex. 3 and -1/3, 5/6 and -6/5, etc.)

1) Determine the slope (m)

When we look at the given line, [tex]y=-2x-1[/tex], we can identify that -2 is in the place of m, the slope of the line. Because perpendicular lines are negative reciprocals of each other, we know that a line perpendicular to this would have a slope of [tex]\frac{1}{2}[/tex]. Plug this into [tex]y=mx+b[/tex]:

[tex]y=\frac{1}{2} x+b[/tex]

2) Determine the y-intercept (b)

[tex]y=\frac{1}{2} x+b[/tex]

Plug in the given point (1,-2)

[tex]-2=\frac{1}{2}(1)+b\\-2=\frac{1}{2}+b[/tex]

Subtract 1/2 from both sides

[tex]-2-\frac{1}{2}=\frac{1}{2}+b-\frac{1}{2}\\-\frac{5}{2} = b[/tex]

Therefore, the y-intercept of the line is [tex]-\frac{5}{2}[/tex]. Plug this back into [tex]y=\frac{1}{2} x+b[/tex]

[tex]y=\frac{1}{2} x-\frac{5}{2}[/tex]

I hope this helps!