Answer :
Certainly! Let's solve the linear equation [tex]\( y + 2x = 8 \)[/tex].
### Step-by-Step Solution:
1. Express [tex]\( y \)[/tex] in terms of [tex]\( x \)[/tex]:
Start with the given equation:
[tex]\[ y + 2x = 8 \][/tex]
To isolate [tex]\( y \)[/tex], subtract [tex]\( 2x \)[/tex] from both sides:
[tex]\[ y = 8 - 2x \][/tex]
2. Find the value of [tex]\( y \)[/tex] for a specific value of [tex]\( x \)[/tex]:
- First Case: Let [tex]\( x = 0 \)[/tex]:
[tex]\[ y = 8 - 2(0) \][/tex]
Simplify the equation:
[tex]\[ y = 8 \][/tex]
Thus, when [tex]\( x = 0 \)[/tex], [tex]\( y \)[/tex] is 8. We have the point [tex]\( (0, 8) \)[/tex].
- Second Case: Let [tex]\( x = 2 \)[/tex]:
[tex]\[ y = 8 - 2(2) \][/tex]
Simplify the equation:
[tex]\[ y = 4 \][/tex]
Thus, when [tex]\( x = 2 \)[/tex], [tex]\( y \)[/tex] is 4. We have the point [tex]\( (2, 4) \)[/tex].
### Conclusion:
For the linear equation [tex]\( y + 2x = 8 \)[/tex]:
- When [tex]\( x = 0 \)[/tex], [tex]\( y = 8 \)[/tex]. This gives us the point [tex]\( (0, 8) \)[/tex].
- When [tex]\( x = 2 \)[/tex], [tex]\( y = 4 \)[/tex]. This gives us the point [tex]\( (2, 4) \)[/tex].
So, the coordinates obtained are:
[tex]\[ (0, 8) \quad \text{and} \quad (2, 4) \][/tex]
These points tell us how [tex]\( y \)[/tex] changes with [tex]\( x \)[/tex] for the given linear equation.
### Step-by-Step Solution:
1. Express [tex]\( y \)[/tex] in terms of [tex]\( x \)[/tex]:
Start with the given equation:
[tex]\[ y + 2x = 8 \][/tex]
To isolate [tex]\( y \)[/tex], subtract [tex]\( 2x \)[/tex] from both sides:
[tex]\[ y = 8 - 2x \][/tex]
2. Find the value of [tex]\( y \)[/tex] for a specific value of [tex]\( x \)[/tex]:
- First Case: Let [tex]\( x = 0 \)[/tex]:
[tex]\[ y = 8 - 2(0) \][/tex]
Simplify the equation:
[tex]\[ y = 8 \][/tex]
Thus, when [tex]\( x = 0 \)[/tex], [tex]\( y \)[/tex] is 8. We have the point [tex]\( (0, 8) \)[/tex].
- Second Case: Let [tex]\( x = 2 \)[/tex]:
[tex]\[ y = 8 - 2(2) \][/tex]
Simplify the equation:
[tex]\[ y = 4 \][/tex]
Thus, when [tex]\( x = 2 \)[/tex], [tex]\( y \)[/tex] is 4. We have the point [tex]\( (2, 4) \)[/tex].
### Conclusion:
For the linear equation [tex]\( y + 2x = 8 \)[/tex]:
- When [tex]\( x = 0 \)[/tex], [tex]\( y = 8 \)[/tex]. This gives us the point [tex]\( (0, 8) \)[/tex].
- When [tex]\( x = 2 \)[/tex], [tex]\( y = 4 \)[/tex]. This gives us the point [tex]\( (2, 4) \)[/tex].
So, the coordinates obtained are:
[tex]\[ (0, 8) \quad \text{and} \quad (2, 4) \][/tex]
These points tell us how [tex]\( y \)[/tex] changes with [tex]\( x \)[/tex] for the given linear equation.
