Question

Are the lines parallel? $$ y=2+3(x+5) ; y=2+4(x+5) $$

   Are the lines parallel?
$$
y=2+3(x+5) ; y=2+4(x+5)
$$

Algebra Form and Function

Algebra Form and Function

William G. McCallum,… 1st Edition

Chapter 5, Problem 37

Instant Answer

Solved by Expert Nick Johnson

04/05/2022

Step 1

The first equation is $y = 2 + 3(x + 5)$. Distributing the 3, we get $y = 3x + 15 + 2$, which simplifies to $y = 3x + 17$. The second equation is $y = 2 + 4(x + 5)$. Distributing the 4, we get $y = 4x + 20 + 2$, which simplifies to $y = 4x + 22$. Show more…

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Are the lines parallel? $$ y=2+3(x+5) ; y=2+4(x+5) $$

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Key Concepts

Slope of a Line

The slope of a line is a measure of its steepness, usually calculated as the ratio of the change in y to the change in x. In this context, identifying the slope is essential because it determines how the line rises or falls as it moves horizontally.

Parallel Lines

Parallel lines are lines in the same plane that never intersect. For two lines to be parallel, they must have the same slope. This concept is fundamental in checking whether two linear equations represent lines that do not cross each other.

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