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

To find the equation of a line that is parallel to another line, both lines must have the same slope. Since Mallory's first line has a slope of 13, the next parallel line will also have a slope of 13. 

The general equation of a line is:

\[
y = mx + b
\]

where \(m\) is the slope and \(b\) is the y-intercept. For the new line, we already know:
- The slope \(m = 13\)
- The y-intercept \(b = 2\) (since the line crosses the y-axis at 2)

Thus, the equation of the next parallel line is:

\[
y = 13x + 2
\]

This matches the response: **y = 13x + 2**.

Would you like more details or have any questions?

Here are 5 related questions:
1. How do you determine if two lines are parallel based on their equations?
2. What happens if the slope of a line is zero? What would the graph look like?
3. How would the equation change if the line crossed the y-axis at -2 instead?
4. What is the effect of changing the y-intercept on the position of a line?
5. How do you find the slope of a line if you're given two points on the line?

**Tip:** To determine the slope of a line from its equation, look at the coefficient of \(x\) in the slope-intercept form \(y = mx + b\).

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?

Learn how to find the equation of a parallel line with slope 13 and y-intercept at 2. This algebraic problem covers the concept of linear equations, slope-intercept form, and parallel line theorem. Suitable for students in Grades 8-10.

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