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In Mathematics / College | 2025-07-07

Find the $y$-intercept for the equation:
y=2 x+6

Asked by carliz0623

Answer (1)

Substitute x = 0 into the equation y = 2 x + 6 .
Calculate y = 2 ( 0 ) + 6 .
Simplify to find y = 6 .
The y -intercept is 6 ​ .

Explanation

Understanding the Problem The equation given is y = 2 x + 6 . We need to find the y -intercept. The y -intercept is the point where the line crosses the y -axis, which occurs when x = 0 .

Substituting x=0 To find the y -intercept, we substitute x = 0 into the equation y = 2 x + 6 . This gives us y = 2 ( 0 ) + 6 .

Simplifying the Equation Simplifying the equation, we have y = 0 + 6 , which means y = 6 .

Finding the y-intercept Therefore, the y -intercept is 6.


Examples
Imagine you are tracking the growth of a plant. The equation y = 2 x + 6 could represent the plant's height ( y ) in inches after x weeks. The y -intercept, 6, tells you that the plant was already 6 inches tall when you started tracking its growth (at week 0). Understanding intercepts helps you interpret the initial conditions in real-world scenarios like this, whether it's plant growth, savings, or any other linear relationship.

Answered by GinnyAnswer | 2025-07-07

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