Question

Coordinate Proofs Quick Check
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Question
Mallory is designing a background print for a logo. She starts the design on a coordinate plane and creates parallel lines diagonally. The first line that she makes has a slope of 13 and crosses through the origin. If she wants the next line to cross the y-axis at 2, what would be the equation of the next parallel line?(1 point)
Responses

y=−13x+2
y equals negative Start Fraction 1 over 3 End Fraction x plus 2

y=3x+2
y equals 3 x plus 2

y=13x+2
y equals Start Fraction 1 over 3 End Fraction x plus 2

y=−3x+2

Answer 1

To find the equation of the next parallel line to Mallory's first line, we need to understand that parallel lines have the same slope.

The first line has a slope of 13 and crosses through the origin, which means its equation is \( y = 13x \).

For the second line, since it is parallel, it will have the same slope of 13, but it will cross the y-axis at 2. Therefore, the equation of the second line can be written as:

\[ y = 13x + 2 \]

So the correct response is:

**y = 13x + 2**