Problem 39 - Algebra 1: Concepts and Skills

Question

Graph the function. $$ f(x)=4 x+1 $$

Step-by-Step Solution

Answer

The graph of the function \(f(x)=4x+1\) is a straight line with a slope of 4 and a y-intercept of 1.

Step 1: Identify the slope and y-intercept

The function \(f(x)=4x+1\) is in the form \(y=mx+b\) where \(m\) is the slope and \(b\) is the y-intercept. Here, \(m=4\) and \(b=1\). So, the slope of the line is 4 and it intersects the y-axis at \(y=1\).

Step 2: Plot the y-intercept

Start by plotting the point where the line intersects the y-axis, that is \(y = 1\). This is plotted on the line \(y\) (vertical axis).

Step 3: Plot the slope

The slope or gradient of the line is 4, indicating that for every unit increase in \(x\), \(y\) increases by 4. From the y-intercept, move 1 unit to the right and 4 units up and draw a point.

Step 4: Draw the line

Now draw a straight line that passes through the two points that have been plotted.