Which equation describes the line that passes through (−3, 1) and is parallel to
the line described by y = 4x + 1?
A.
y
=
−
1
4
x
+
7
4
B.
y
=
4
x
−
11
C.
y
=
4
x
+
13
D.
y
=
−
1
4
x
+
1
4
The equation of a line that is parallel to y = 4x + 1 has the same slope. The slope of y = 4x + 1 is 4.
Using the point-slope form of a linear equation, y - y1 = m(x - x1), where (x1, y1) is a point on the line, and m is the slope, we can plug in the values (-3, 1) and 4 to find the equation:
y - 1 = 4(x - (-3))
y - 1 = 4(x + 3)
y - 1 = 4x + 12
y = 4x + 12 + 1
y = 4x + 13
Therefore, the equation that describes the line that passes through (-3, 1) and is parallel to y = 4x + 1 is y = 4x + 13.
The answer is C. y = 4x + 13.