Question
Isolate the \( y \)-term on the left side of the equation. \[ \begin{array}{l} 6 y-42=0 \\ 6 y=42 \\ y=7 \\ \text { Add } 42 \text { to eact side. } \\ \text { (Simplify your answer. Type an integer or a simpilified fraction) } \\ \text { Thus, the } y \text {-intercept is } \\ \text { (Type an ordered pair.) }\end{array} \]
Ask by Herrera Kelley. in the United States
Feb 03,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
The \( y \)-intercept is \( (0, 7) \).
Solution
To find the \( y \)-intercept of the equation \( 6y - 42 = 0 \), follow these steps:
1. **Isolate the \( y \)-term:**
\[
6y - 42 = 0
\]
Add \( 42 \) to both sides:
\[
6y = 42
\]
2. **Solve for \( y \):**
\[
y = \frac{42}{6} = 7
\]
3. **Determine the \( y \)-intercept:**
The \( y \)-intercept occurs where \( x = 0 \). Therefore, the ordered pair is:
\[
(0, 7)
\]
**Final Answer:**
The \( y \)-intercept is \( (0, 7) \).
Reviewed and approved by the UpStudy tutoring team
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Simplify this solution Mind Expander
To isolate the \( y \)-term on the left side of the equation, we start with the original equation: \( 6y - 42 = 0 \). By adding 42 to both sides, we get \( 6y = 42 \). Next, we divide both sides by 6, which gives us \( y = 7 \). Therefore, the \( y \)-intercept can be expressed as the ordered pair \( (0, 7) \). To reinforce this process, think of the equation as a balancing act! Whatever you do to one side, you must do to the other to keep it perfectly balanced. Mistakes often involve miscalculating basic operations or forgetting to apply them to both sides, so staying vigilant is key!
