Find the $y$-intercept of the line represented by the equation below.

$-12=-2 x-4 y$

The y -intercept of the line represented by the equation − 12 = − 2 x − 4 y is 3. This means that the line crosses the y -axis at the point ( 0 , 3 ) .
;

Answered by Anonymous | 2025-07-04

Substitute x = 0 into the equation − 12 = − 2 x − 4 y .
Simplify the equation to − 12 = − 4 y .
Divide both sides by − 4 to solve for y : y = 3 .
The y -intercept is 3 ​ .

Explanation

Understanding the Problem We are given the equation of a line: − 12 = − 2 x − 4 y . 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: − 12 = − 2 ( 0 ) − 4 y

Simplifying the Equation Now we simplify the equation: − 12 = 0 − 4 y
− 12 = − 4 y

Solving for y To solve for y , we divide both sides of the equation by − 4 : − 4 − 12 ​ = − 4 − 4 y ​
3 = y
So, y = 3 .

Finding the y -intercept The y -intercept is the point where the line crosses the y -axis, which is ( 0 , y ) . Since we found that y = 3 , the y -intercept is ( 0 , 3 ) . Therefore, the y -coordinate of the y -intercept is 3.


Examples
Understanding the y-intercept is crucial in many real-world scenarios. For example, in a linear cost function, where 'x' represents the number of items produced and 'y' represents the total cost, the y-intercept indicates the fixed cost - the cost incurred even when no items are produced. If the equation is − 12 = − 2 x − 4 y , rearranging it to slope-intercept form gives y = − 0.5 x − 3 . Here, the y-intercept of -3 (or ( 0 , − 3 ) ) would represent an initial debt or cost of $3 before any items are produced. Similarly, in a sales context, if 'x' is the number of sales calls made and 'y' is the revenue, the y-intercept could represent the initial revenue before any calls are made.

Answered by GinnyAnswer | 2025-07-04