Answer :
Let's solve the problem step by step.
We are given the equation [tex]\( y = 100 - 2x \)[/tex].
1. Identify the change in [tex]\( x \)[/tex]:
- We are told that [tex]\( x \)[/tex] increases by 3.
2. Find the effect on [tex]\( y \)[/tex]:
- To see how changing [tex]\( x \)[/tex] affects [tex]\( y \)[/tex], substitute [tex]\( x + 3 \)[/tex] into the equation:
[tex]\[ y = 100 - 2(x + 3). \][/tex]
3. Simplify the expression:
- Distribute the [tex]\(-2\)[/tex] across the terms inside the parentheses:
[tex]\[ y = 100 - 2x - 6. \][/tex]
- Simplify further to get:
[tex]\[ y = (100 - 6) - 2x = 94 - 2x. \][/tex]
4. Find the change in [tex]\( y \)[/tex]:
- Initially, [tex]\( y = 100 - 2x \)[/tex].
- After the increase in [tex]\( x \)[/tex], [tex]\( y = 94 - 2x \)[/tex].
- The change in [tex]\( y \)[/tex] is the difference between these two expressions:
[tex]\[ \text{Change in } y = (94 - 2x) - (100 - 2x). \][/tex]
5. Simplify to find the change:
- The terms involving [tex]\( x \)[/tex] cancel out:
[tex]\[ \text{Change in } y = 94 - 100 = -6. \][/tex]
Therefore, the corresponding change in the [tex]\( y \)[/tex]-value is [tex]\(-6\)[/tex], which means the answer is option (d) [tex]\(-6\)[/tex].
We are given the equation [tex]\( y = 100 - 2x \)[/tex].
1. Identify the change in [tex]\( x \)[/tex]:
- We are told that [tex]\( x \)[/tex] increases by 3.
2. Find the effect on [tex]\( y \)[/tex]:
- To see how changing [tex]\( x \)[/tex] affects [tex]\( y \)[/tex], substitute [tex]\( x + 3 \)[/tex] into the equation:
[tex]\[ y = 100 - 2(x + 3). \][/tex]
3. Simplify the expression:
- Distribute the [tex]\(-2\)[/tex] across the terms inside the parentheses:
[tex]\[ y = 100 - 2x - 6. \][/tex]
- Simplify further to get:
[tex]\[ y = (100 - 6) - 2x = 94 - 2x. \][/tex]
4. Find the change in [tex]\( y \)[/tex]:
- Initially, [tex]\( y = 100 - 2x \)[/tex].
- After the increase in [tex]\( x \)[/tex], [tex]\( y = 94 - 2x \)[/tex].
- The change in [tex]\( y \)[/tex] is the difference between these two expressions:
[tex]\[ \text{Change in } y = (94 - 2x) - (100 - 2x). \][/tex]
5. Simplify to find the change:
- The terms involving [tex]\( x \)[/tex] cancel out:
[tex]\[ \text{Change in } y = 94 - 100 = -6. \][/tex]
Therefore, the corresponding change in the [tex]\( y \)[/tex]-value is [tex]\(-6\)[/tex], which means the answer is option (d) [tex]\(-6\)[/tex].
