Question
\begin{tabular}{|l|l|l|}\hline Write each equation in slope-intercept form. \\ \hline 7. \( x+y=6 \) & 8. \( 5 x+2 y=-2 \) & 9. \( 2 x-4 y=28 \) \\ & & \\ \hline\end{tabular}
Ask by Carlson Frazier. in Guam
Feb 24,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The equations in slope-intercept form are:
7. \( y = -x + 6 \)
8. \( y = -\frac{5}{2}x - 1 \)
9. \( y = \frac{1}{2}x - 7 \)
Solution
We want to rewrite each equation in slope-intercept form, y = mx + b.
For equation 7:
x + y = 6
Subtract x from both sides:
y = –x + 6
For equation 8:
5x + 2y = –2
Subtract 5x from both sides:
2y = –5x – 2
Divide both sides by 2:
y = –(5/2)x – 1
For equation 9:
2x – 4y = 28
Subtract 2x from both sides:
–4y = –2x + 28
Divide both sides by –4:
y = (2/4)x – 7
Simplify (2/4) to (1/2):
y = (1/2)x – 7
Thus, the equations in slope-intercept form are:
7. y = –x + 6
8. y = –(5/2)x – 1
9. y = (1/2)x – 7
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Simplify this solution Bonus Knowledge
To convert each equation into slope-intercept form (y = mx + b), we isolate y on one side. For the first equation: 1. \( x + y = 6 \) - Subtract \( x \) from both sides: - \( y = -x + 6 \) For the second equation: 2. \( 5x + 2y = -2 \) - Subtract \( 5x \) from both sides: - \( 2y = -5x - 2 \) - Divide everything by 2: - \( y = -\frac{5}{2}x - 1 \) For the third equation: 3. \( 2x - 4y = 28 \) - Subtract \( 2x \) from both sides: - \( -4y = -2x + 28 \) - Divide everything by -4: - \( y = \frac{1}{2}x - 7 \) Thus, the equations in slope-intercept form are: 1. \( y = -x + 6 \) 2. \( y = -\frac{5}{2}x - 1 \) 3. \( y = \frac{1}{2}x - 7 \)
