Certainly! Let's solve the equation step by step:
We are given the equation:
[tex]\[ 4y - 7 = 0 \][/tex]
To solve for [tex]\( y \)[/tex], we need to isolate [tex]\( y \)[/tex] on one side of the equation. Here are the steps:
1. Rewrite the equation to make it clearer:
[tex]\[ 4y - 7 = 0 \][/tex]
2. Add 7 to both sides of the equation to move the constant term to the right side.
[tex]\[ 4y - 7 + 7 = 0 + 7 \][/tex]
Simplifying this, we get:
[tex]\[ 4y = 7 \][/tex]
3. Divide both sides of the equation by 4 to solve for [tex]\( y \)[/tex]:
[tex]\[ y = \frac{7}{4} \][/tex]
So, the solution to the equation [tex]\( 4y - 7 = 0 \)[/tex] is:
[tex]\[ y = \frac{7}{4} \][/tex]
This means that in the real coordinate plane [tex]\( \mathbb{R}^2 \)[/tex], the set of all points [tex]\((x, y)\)[/tex] that satisfy the equation [tex]\( 4y - 7 = 0 \)[/tex] consists of all points where the [tex]\( y \)[/tex]-coordinate is [tex]\( \frac{7}{4} \)[/tex]. Therefore, the set can be described as:
[tex]\[ \operatorname{R}\left\{(x, y) \in \mathbb{R}^2 \mid y = \frac{7}{4} \right\} \][/tex]
This represents a horizontal line in the coordinate plane where [tex]\( y \)[/tex] is always [tex]\( \frac{7}{4} \)[/tex], and [tex]\( x \)[/tex] can be any real number.
