Problem 43 - Algebra 1: Concepts and Skills

Question

Graph the function. $$ f(x)=2 x+3 $$

Step-by-Step Solution

Answer

The line for the graph of the given function \(f(x)=2x+3\) starts at the y-intercept (0,3) and moves up 2 units for each unit to the right, as the slope of the line is 2.

Step 1: Identify the Slope

In the given function \(f(x) = 2x + 3\), the coefficient of \(x\) is 2, so the slope (\(m\)) of the line is 2. This means for every step increase in \(x\), \(f(x)\) (or \(y\)) will increase by 2 steps.

Step 2: Identify the Y-Intercept

In the function, the constant is 3, which represents the y-intercept (\(c\)). This is the point at which the line crosses the y-axis. This means that when \(x = 0\), \(f(x) = 3\). Thus, the line crosses the y-axis at (0,3).

Step 3: Plot the Function on a Graph

Begin at the y-intercept on the y-axis at (0,3), since it's known that the line crosses there. As the slope is 2, for each step to the right on the x-axis, go up by 2 steps to get the next point on the line. Then, draw a straight line through these points to graph the function \(f(x) = 2x + 3\).