Question
Write each equation in the slope-intercept form, \( y=m x+b \) \[ \begin{array}{l}x+2=y \\ y-x=-3\end{array} \rightarrow \begin{array}{c}y=x+2 \\ y=\square\end{array} \]
Ask by Morrison Cole. in the United States
Feb 03,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
The equations in slope-intercept form are:
\[
\begin{array}{c}
y = x + 2 \\
y = x - 3
\end{array}
\]
Solution
Rewrite the equation by following steps:
- step0: Rewrite in slope-intercept form:
\(y-x=-3\)
- step1: Move the expression to the right side:
\(y=-3+x\)
- step2: Rearrange the terms:
\(y=x-3\)
Rewrite the equation \( x+2=y \).
Rewrite the equation by following steps:
- step0: Rewrite in slope-intercept form:
\(x+2=y\)
- step1: Move the expression to the right side:
\(2=y-x\)
- step2: Move the expression to the left side:
\(2-y=-x\)
- step3: Move the constant to the right side:
\(-y=-x-2\)
- step4: Divide both sides:
\(y=x+2\)
Let's convert each equation into slope-intercept form \( y = mx + b \).
1. For the first equation \( x + 2 = y \):
- This can be rewritten directly as:
\[
y = x + 2
\]
2. For the second equation \( y - x = -3 \):
- Rearranging gives:
\[
y = x - 3
\]
Thus, the equations in slope-intercept form are:
\[
\begin{array}{c}
y = x + 2 \\
y = x - 3
\end{array}
\]
Reviewed and approved by the UpStudy tutoring team
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Simplify this solution Bonus Knowledge
To rewrite the first equation \( x + 2 = y \) in slope-intercept form, you have it correct as \( y = x + 2 \). Now, let's convert the second equation \( y - x = -3 \). To get \( y \) by itself, add \( x \) to both sides: \[ y = x - 3 \] So, putting it all together, we have: \[ y = x + 2 \] \[ y = x - 3 \]
