Question

Write an equation that passes through the point (3,2) and is perpendicular to the line y=-1x+5.

a) y = 1x - 1
b) y = -1x + 11
c) y = 2x - 4
d) y = 4x - 6

Answer 1

The equation that passes through the point (3,2) and is perpendicular to the line y=-1x+5 is y = x - 1.

Step-by-step explanation:

To find an equation that is perpendicular to a given line and passes through a given point, we first need to determine the slope of the given line. In the equation y = -1x + 5, the slope is -1. The slope of a line perpendicular to this line will be the negative reciprocal of -1, which is 1.

Now that we know the slope of the perpendicular line is 1, we can use the point-slope form of the equation to find 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.

Substituting the coordinates of the given point (3, 2) into the equation, we get y - 2 = 1(x - 3). Simplifying this equation gives us y - 2 = x - 3. Adding 2 to both sides of the equation gives us the final equation: y = x - 1.