Answer:
y = -x + 3
Step-by-step explanation:
To find the equation of a line perpendicular to y = x + 1 that passes through the point (2, 1), follow these steps:
1. Identify the slope of the given line y = x + 1. In this case, the slope (m) is 1.
2. The slope of a line perpendicular to another line is the negative reciprocal of the original slope. So, the perpendicular slope is -1/1 or -1.
3. Now, use the point-slope form of a linear equation: y - y1 = m(x - x1), where (x1, y1) is the given point.
Substitute the values:
y - 1 = -1 * (x - 2)
4. Simplify the equation to slope-intercept form y = mx + b:
y - 1 = -x + 2
y = -x + 3
So, the equation of the line perpendicular to y = x + 1 that passes through (2, 1) is y = -x + 3.
