Find the y-intercept of the line represented by the equation below:

4x - 4y = 4

To find the y-intercept of the line represented by 4 x − 4 y = 4 , substitute x = 0 into the equation, resulting in y = − 1 . Thus, the y-intercept is − 1 . The point where the line crosses the y-axis is (0, -1).
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Answered by Anonymous | 2025-07-04

To find the y-intercept, set x = 0 in the equation 4 x − 4 y = 4 .
Substitute x = 0 into the equation: 4 ( 0 ) − 4 y = 4 , which simplifies to − 4 y = 4 .
Solve for y : y = − 4 4 ​ = − 1 .
The y-intercept is − 1 ​ .

Explanation

Understanding the Problem We are given the equation of a line: 4 x − 4 y = 4 . Our goal is to find the y-intercept of this line. 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 of the line: 4 ( 0 ) − 4 y = 4

Solving for y This simplifies to: − 4 y = 4 Now, we solve for y by dividing both sides of the equation by − 4 : − 4 − 4 y ​ = − 4 4 ​ y = − 1

Finding the y-intercept Therefore, the y-intercept is the point ( 0 , − 1 ) . The y-coordinate of the y-intercept is − 1 .


Examples
Understanding y-intercepts is crucial in many real-world applications. For example, in a business model, the y-intercept of a cost function can represent the fixed costs, which are the costs incurred even when no units are produced. If a company's cost equation is C = 5 x + 20 , where C is the total cost and x is the number of units produced, the y-intercept of 20 indicates that the company has fixed costs of $20, regardless of how many units they produce. This concept helps in making informed financial decisions.

Answered by GinnyAnswer | 2025-07-04