To find the equation of a line that is perpendicular to a given line, we need to determine the slope of the perpendicular line.
The given line has a slope of -2, so the perpendicular line will have a slope that is the negative reciprocal of -2. To find the negative reciprocal, we flip the fraction and change the sign. The negative reciprocal of -2 is 1/2.
Now that we have the slope of the perpendicular line, we can use the point-slope form of a linear equation to write the equation of the line. The point-slope form is given by: y - y1 = m(x - x1), where m is the slope and (x1, y1) is a point on the line.
Using the point (0, -2) and the slope 1/2, we can write the equation: y - (-2) = 1/2(x - 0)
Simplifying the equation: y + 2 = 1/2x
Rearranging the equation to the slope-intercept form (y = mx + b) by subtracting 2 from both sides: y = 1/2x - 2
Therefore, the equation of the line that is perpendicular to y = -2x + 5 and passes through the point (0, -2) is y = 1/2x - 2.
What is the equation of the line that is perpendicular to y=-2x+5 and passes through the point (0,-2)?
1 answer