Question

How do you write an equation that passes through (2,2), perpendicular to y=2x+4(with steps pls)

Answer 1

To write the equation of a line that is perpendicular to y=2x+4 and passes through the point (2,2), find the negative reciprocal of the original slope, which is -1/2, and use the point-slope form to create the equation y = -1/2x + 3.

Step-by-step explanation:

To write an equation that passes through the point (2,2) and is perpendicular to the equation y=2x+4, one must follow these steps:

1. Identify the slope (m) of the given line, which is 2 (since y=mx+b and m=2 in the equation y=2x+4).
2. Find the slope of the line that is perpendicular to the given line. Perpendicular lines have slopes that are negative reciprocals of each other. Thus, the slope of the perpendicular line is -1/2.
3. Use the point-slope form of the equation of a line, which is y - y1 = m(x - x1), where m is the slope and (x1, y1) is the point through which the line passes. Substituting -1/2 for m and (2,2) for (x1, y1), we get: y - 2 = -1/2(x - 2).
4. Rewrite the equation in slope-intercept form, y = mx + b, to find b. Simplifying the equation from step 3, we get y - 2 = -1/2x + 1, and then y = -1/2x + 3.

Therefore, the equation of the line that is perpendicular to y=2x+4 and passes through (2,2) is y = -1/2x + 3.