Which equation describes a line that passes through (0, 3) and is perpendicular to
the line described by y = −5x − 4?
A.
y
=
5
x
+
3
B.
y
=
1
5
x
+
3
C.
y
=
−
5
x
+
3
D.
y
=
−
1
5
x
+
3
To find an equation that describes a line perpendicular to y = -5x - 4, we need to find the negative reciprocal of the slope of the given line. The slope of the given line is -5, so the negative reciprocal is 1/5.
We also know that the new line passes through the point (0, 3).
Using the slope-intercept form of a line, y = mx + b, where m is the slope and b is the y-intercept, we can substitute the slope and the given point to find the equation.
The equation of the line can be written as:
y = 1/5x + b
To find b, we substitute the coordinates (0, 3) into the equation:
3 = 1/5(0) + b
3 = 0 + b
b = 3
So the equation of the line that passes through (0, 3) and is perpendicular to y = -5x - 4 is:
y = 1/5x + 3
Therefore, the answer is:
B. y = 1/5x + 3