Question

Which of the following equations defines a line that is parallel to the line
y
=
2
3
x
+
4
?
A.
4
x
−
6
y
=
9
B.
6
x
+
4
y
=
9
C.
6
x
−
4
y
=
9
D.
4
x
+
6
y
=
9

Answer 1

The equation y = 2/3x + 4 is in slope-intercept form, y = mx + b, where m is the slope. The slope of this line is 2/3.

To find a line that is parallel to this line, it must have the same slope of 2/3.

Looking at the given options:
A. 4x - 6y = 9 does not have a slope of 2/3.
B. 6x + 4y = 9 does not have a slope of 2/3.
C. 6x - 4y = 9 does not have a slope of 2/3.
D. 4x + 6y = 9 has a slope of 4/6, which simplifies to 2/3.

Therefore, the equation 4x + 6y = 9 defines a line that is parallel to y = 2/3x + 4. The answer is (D).