Certainly! Let's analyze and understand the given linear equation step by step.
Given Equation:
[tex]\[ 5x + 2y = 1 \][/tex]
Let's break it down:
1. Identify Coefficients and Constants:
- The coefficient of \( x \) is \( 5 \).
- The coefficient of \( y \) is \( 2 \).
- The constant term on the right side of the equation is \( 1 \).
So, we have:
[tex]\[ a = 5 \][/tex]
[tex]\[ b = 2 \][/tex]
[tex]\[ c = 1 \][/tex]
2. Standard Form:
The equation \( 5x + 2y = 1 \) is already in its standard linear form:
[tex]\[ ax + by = c \][/tex]
For this specific equation:
[tex]\[ 5x + 2y = 1 \][/tex]
This tells us that for each unit increase in \( x \), we need to adjust \( y \) accordingly to maintain the balance of 1 on the right-hand side of the equation.
3. Interpretation:
The equation represents a straight line on a Cartesian plane. The coefficients provide insight into the slope (steepness) and intercepts of the line, but we're primarily concerned with identifying the coefficients and the constant for now.
To summarize, the coefficients \( a \), \( b \), and constant \( c \) for the given linear equation are:
[tex]\[ a = 5 \][/tex]
[tex]\[ b = 2 \][/tex]
[tex]\[ c = 1 \][/tex]
Thus, the equation [tex]\( 5x + 2y = 1 \)[/tex] succinctly represents these values.
