To find the value of [tex]\( y \)[/tex] for a given [tex]\( x \)[/tex] in the linear equation [tex]\( y = 2x + 3 \)[/tex], let's break down the steps for a specific example. Suppose we are solving for [tex]\( x = 15 \)[/tex].
### Step-by-Step Solution:
1. Identify the equation:
The given equation is:
[tex]\[
y = 2x + 3
\][/tex]
2. Substitute [tex]\( x \)[/tex] with the given value:
Here, [tex]\( x = 15 \)[/tex]. So, substitute [tex]\( x \)[/tex] in the equation:
[tex]\[
y = 2(15) + 3
\][/tex]
3. Perform the multiplication:
First, compute [tex]\( 2 \times 15 \)[/tex]:
[tex]\[
2 \times 15 = 30
\][/tex]
4. Add the constant term:
Now, add 3 to the result:
[tex]\[
30 + 3 = 33
\][/tex]
So, when [tex]\( x = 15 \)[/tex], the value of [tex]\( y \)[/tex] is:
[tex]\[
y = 33
\][/tex]
### Conclusion:
For the given value of [tex]\( x = 15 \)[/tex], the corresponding value of [tex]\( y \)[/tex] in the linear equation [tex]\( y = 2x + 3 \)[/tex] is:
[tex]\[
y = 33
\][/tex]
Thus, the point [tex]\((15, 33)\)[/tex] lies on the line described by the equation [tex]\( y = 2x + 3 \)[/tex].
