Question

graph the function $g(x) = -2x - 3$.

Explanation:

Step1: Identify the slope and y-intercept

The function \( g(x) = -2x - 3 \) is in slope - intercept form \( y=mx + b \), where \( m \) is the slope and \( b \) is the y - intercept. Here, \( m=-2 \) and \( b = - 3 \).

Step2: Plot the y-intercept

The y - intercept is \( b=-3 \), so we plot the point \( (0,-3) \) on the y - axis.

Step3: Use the slope to find another point

The slope \( m=-2=\frac{-2}{1} \). From the point \( (0,-3) \), we move down 2 units (because the numerator of the slope is - 2) and then 1 unit to the right (because the denominator of the slope is 1). This gives us the point \( (1,-5) \). We can also move up 2 units and 1 unit to the left from \( (0,-3) \) to get the point \( (-1,-1) \).

Step4: Draw the line

Draw a straight line through the points we have plotted (e.g., \( (0,-3) \), \( (1,-5) \), \( (-1,-1) \)) to graph the function \( g(x)=-2x - 3 \).

Answer:

To graph \( g(x)=-2x - 3 \), plot the y - intercept \( (0,-3) \), then use the slope \( - 2 \) to find additional points (e.g., \( (1,-5) \) or \( (-1,-1) \)) and draw a straight line through these points. The line should have a negative slope, passing through \( (0,-3) \) and other points determined by the slope.