Certainly, let's work through this question step-by-step.
We need to determine whether the point [tex]\( P(-4, -1) \)[/tex] satisfies the equation [tex]\( 4x - 2y = 6 \)[/tex].
1. Identify the coordinates of the point [tex]\( P \)[/tex]:
- [tex]\( x = -4 \)[/tex]
- [tex]\( y = -1 \)[/tex]
2. Substitute the coordinates of the point [tex]\( P \)[/tex] into the equation [tex]\( 4x - 2y = 6 \)[/tex]:
[tex]\[
4x - 2y
\][/tex]
3. Plug in [tex]\( x = -4 \)[/tex] and [tex]\( y = -1 \)[/tex] into the left side of the equation:
[tex]\[
4(-4) - 2(-1)
\][/tex]
4. Evaluate the expression [tex]\( 4(-4) - 2(-1) \)[/tex]:
- First, calculate [tex]\( 4 \times -4 \)[/tex]:
[tex]\[
4 \times -4 = -16
\][/tex]
- Next, calculate [tex]\( -2 \times -1 \)[/tex]:
[tex]\[
-2 \times -1 = 2
\][/tex]
- Then, add the results:
[tex]\[
-16 + 2 = -14
\][/tex]
5. The result of the expression after substituting [tex]\( x \)[/tex] and [tex]\( y \)[/tex] is:
[tex]\[
4(-4) - 2(-1) = -14
\][/tex]
6. Compare this result to the right side of the original equation [tex]\( 4x - 2y = 6 \)[/tex]:
[tex]\[
-14 \neq 6
\][/tex]
7. Since [tex]\(-14\)[/tex] is not equal to [tex]\(6\)[/tex], the point [tex]\( P(-4, -1) \)[/tex] does not satisfy the equation [tex]\( 4x - 2y = 6 \)[/tex].
So the point [tex]\( P(-4, -1) \)[/tex] does not lie on the line represented by the equation [tex]\( 4x - 2y = 6 \)[/tex]. The equation evaluates to [tex]\(-14\)[/tex] when [tex]\( x \)[/tex] is [tex]\(-4\)[/tex] and [tex]\( y \)[/tex] is [tex]\(-1\)[/tex], which is not equal to 6. Therefore, [tex]\( P(-4, -1) \)[/tex] does not satisfy the equation.
