To determine if the point [tex]\((0,-2)\)[/tex] is a solution to the equation [tex]\(y = 7x - 2\)[/tex], let's verify it step-by-step:
1. Identify the given point and equation:
- The given point is [tex]\((0, -2)\)[/tex].
- The given equation is [tex]\(y = 7x - 2\)[/tex].
2. Substitute the [tex]\(x\)[/tex] and [tex]\(y\)[/tex] values from the point into the equation:
- [tex]\(x = 0\)[/tex]
- [tex]\(y = -2\)[/tex]
So, substitute [tex]\(x = 0\)[/tex] into the equation [tex]\(y = 7x - 2\)[/tex]:
[tex]\[
y = 7(0) - 2
\][/tex]
3. Simplify the equation after substitution:
[tex]\[
y = 7 \cdot 0 - 2
\][/tex]
[tex]\[
y = 0 - 2
\][/tex]
[tex]\[
y = -2
\][/tex]
4. Compare the calculated [tex]\(y\)[/tex] value with the given [tex]\(y\)[/tex] value:
- From the calculation, we found [tex]\(y = -2\)[/tex].
- The given point's [tex]\(y\)[/tex] value is also [tex]\(-2\)[/tex].
Since both [tex]\(y\)[/tex] values match, the point [tex]\((0, -2)\)[/tex] satisfies the equation [tex]\(y = 7x - 2\)[/tex].
Thus, the point [tex]\((0, -2)\)[/tex] is a solution to the equation [tex]\(y = 7x - 2\)[/tex].
Therefore, the answer is yes.
