To find the equation of a line that passes through the point (2, -1) and is perpendicular to the graph of the equation y = -2x - 1, you can use the following steps:
Determine the slope of the given equation: y = -2x - 1. In this equation, the coefficient of x is -2, which represents the slope of the line.
Find the negative reciprocal of the slope to get the slope of the perpendicular line. The negative reciprocal of -2 is 1/2.
Use the point-slope form of a linear equation to write the equation of the perpendicular line. The point-slope form is:
y - y1 = m(x - x1),
where (x1, y1) is the given point, and m is the slope.
Plugging in the values:
y - (-1) = (1/2)(x - 2).
Simplify:
y + 1 = (1/2)(x - 2).
If you want to write the equation in slope-intercept form (y = mx + b), you can rearrange it:
y + 1 = (1/2)(x - 2).
Distribute (1/2) on the right side:
y + 1 = (1/2)x - 1.
Subtract 1 from both sides:
y = (1/2)x - 1 - 1.
y = (1/2)x - 2.
So, the equation of the line that passes through the point (2, -1) and is perpendicular to the graph of y = -2x - 1 is:
y = (1/2)x - 2.