Question

Graph the function. $$ g(x)=-\frac{1}{2} x-3 $$

Short answer

The graph is a straight line that passes through the points (0, -3) and (1, -3.5) and decreases as it moves from left to right, meaning the slope is negative.

Step-by-step solution

Identify the slope and the y-intercept

The function \( g(x) = -\frac{1}{2}x - 3 \) is in slope-intercept form, also known as \(y = mx + b\), where \(m\) is the slope of the line and \(b\) is the y-intercept. The slope \(m\) of this function is \(-\frac{1}{2}\) and the y-intercept \(b\) is -3.

Start the graph

To start graphing, first plot the y-intercept, which is the point (0, -3) on the y-axis.

Plot the slope

The slope \(-\frac{1}{2}\) means for every 1 unit increase in \(x\), \(y\) decreases by \(\frac{1}{2}\). From the y-intercept, move one unit to the right (increase of \(x\)), and then half of a unit down (decrease of \(y\)). This gives another point you can draw on the graph, namely (1, -3.5).

Draw the line

Finally, a straight line is drawn that passes through these points. This line represents the function \(g(x) = -\frac{1}{2}x - 3\).