Question

Find the equation of the line that passes through (1,3) and is perpendicular to

y
=
2
x
−
1
.
Leave your answer in the form
y
=
m
x
+
c

Answer 1

To find the equation of a line that is perpendicular to y = 2x - 1 and passes through (1,3), we use the point-slope form of the equation. The equation of the perpendicular line is y = (-1/2)x + 3/2.

Step-by-step explanation:

To find the equation of a line that is perpendicular to y = 2x - 1 and passes through (1,3), we need to determine the slope of the line and use the point-slope form of the equation of a line. The given line has a slope of 2, so the perpendicular line will have a slope of -1/2 (the negative reciprocal of 2). Now we can use the point-slope form, which is y - y1 = m(x - x1), where (x1, y1) is the given point and m is the slope. Plugging in the values, we get y - 3 = (-1/2)(x - 1). Simplifying, we have y = (-1/2)x + 3/2 as the equation of the line.