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When we talk about substituting a variable, we're essentially replacing a variable with a specific number. In the given function, we have a variable "x" in the expression \(g(x) = 53x - 5\). To find \(g(3)\), we replace "x" with 3. This change is essential because it allows us to evaluate the function for a specific input.

• Identify the variable in the function.
• Replace the variable with a specified number.
• Solve the resulting equation.

By substituting 3 for \(x\), we transform the equation into a simple arithmetic problem: \(53 \times 3 - 5\). This method makes abstract equations concrete, providing specific numerical answers.

Linear functions are special because they create a straight line when plotted on a graph. The function is typically written in the form \(f(x) = mx + b\), where "m" is the slope, and "b" is the y-intercept. In the function \(g(x) = 53x - 5\), 53 is the slope. This number shows that for each increase in \(x\), \(g(x)\) increases by 53 units. The number -5 is the y-intercept, indicating where the line crosses the y-axis.
The concept of slope is essential in understanding how steep or flat a line is on a graph. A higher absolute value of the slope results in a steeper line. For instance, here the slope is 53, indicating a fairly steep line.
Linear functions are powerful tools in mathematics to describe relationships with constant rates of change. They are simple yet very effective in modeling real-world phenomena.

Algebraic expressions mix letters and numbers along with operations such as addition and multiplication. In our exercise, \(g(x) = 53x - 5\) is the algebraic expression. It uses the variable "x," the number 53, the operation of multiplication, and the subtraction of 5.

• "x" is a variable representing an unknown.
• 53 is a coefficient affecting the variable "x".
• -5 is a constant term.

Evaluating algebraic expressions means finding the value of the expression for a specific variable input. The main operations follow the order of precedence: first, perform multiplication, then subtraction. Understanding algebraic expressions is the foundation of algebra. They are like language sentences where numbers and operations come together to provide meaningful information.