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Are these lines perpendicular, parallel, or neither based on their slopes?

[tex]\[ \begin{array}{l}
6x - 2y = -2 \\
y = 3x + 12
\end{array} \][/tex]

The [tex]\(\square\)[/tex] of their slopes is [tex]\(\square\)[/tex], so the lines are [tex]\(\square\)[/tex].

Sagot :

GinnyAnsweridn
Let's determine the relationship between the lines based on their slopes. Here are the given equations:
[tex]\[ 6x - 2y = -2 \][/tex]
[tex]\[ y = 3x + 12 \][/tex]

First, we need to convert the first equation to the slope-intercept form [tex]\( y = mx + b \)[/tex], where [tex]\( m \)[/tex] is the slope and [tex]\( b \)[/tex] is the y-intercept.

Starting with the equation:
[tex]\[ 6x - 2y = -2 \][/tex]

We isolate [tex]\( y \)[/tex]:
[tex]\[ -2y = -6x - 2 \][/tex]

Divide by -2:
[tex]\[ y = 3x + 1 \][/tex]

From this, we can see that the slope ([tex]\( m \)[/tex]) of the line is 3.

For the second equation:
[tex]\[ y = 3x + 12 \][/tex]

This equation is already in slope-intercept form, and we can identify the slope ([tex]\( m \)[/tex]) of this line as 3.

Now, we compare the slopes of both lines:
- Slope of the first line: 3
- Slope of the second line: 3

The slopes of these lines are equal (both are 3), which means the lines are parallel.

Thus, we can conclude:
The slopes of their slopes is 3, so the lines are parallel.
36917965idn

Answer:

The lines are parallel.

Step-by-step explanation:

When we simplify the first equation, we get 2y=6x+2, which can be simplified into y=3x+2, and because this equation and the second one have the same slope, they are parallel.

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