To determine which pair of equations represents two lines that are parallel, we need to look at the slopes of the lines. Remember that two lines are parallel if they have the same slope.
Let's analyze each pair of equations:
a.
[tex]\[ y = -3x + 4 \][/tex]
[tex]\[ y = 2x + 4 \][/tex]
- The slope of the first line is -3.
- The slope of the second line is 2.
- Since -3 ≠ 2, these lines are not parallel.
b.
[tex]\[ y = 6x + 7 \][/tex]
[tex]\[ y = x - 2 \][/tex]
- The slope of the first line is 6.
- The slope of the second line is 1.
- Since 6 ≠ 1, these lines are not parallel.
c.
[tex]\[ y = 3x - 2 \][/tex]
[tex]\[ y = 3x + 4 \][/tex]
- The slope of both lines is 3.
- Since 3 = 3, these lines are parallel.
d.
[tex]\[ y = 3x - 2 \][/tex]
[tex]\[ y = x + 4 \][/tex]
- The slope of the first line is 3.
- The slope of the second line is 1.
- Since 3 ≠ 1, these lines are not parallel.
Therefore, the pair of equations that represents two lines that are parallel is option c:
[tex]\[ y = 3x - 2 \][/tex]
[tex]\[ y = 3x + 4 \][/tex]
