Final answer:
To graph y = -2/5x - 6, plot the y-intercept at (0, -6) and use the negative slope of -2/5 to find another point by moving right 5 units and down 2 units to (5, -8), then connect the points to show the downward trending line.
Step-by-step explanation:
To graph the equation y = -2/5x - 6, you will need to plot the y-intercept and use the slope to determine the direction and steepness of the line.
First, identify the y-intercept which is the point where the line crosses the y-axis. In this equation, the y-intercept is -6. This point can be plotted directly on the graph at (0, -6).
Next, consider the slope, which is -2/5. A negative slope indicates that the graph will trend downward as x increases. The value of the slope, -2/5, means that for every 5 units you move to the right on the x-axis, you will move 2 units down on the y-axis.
Using the y-intercept and the slope, you can plot a second point starting from (0, -6) by moving 5 units to the right (positive direction along the x-axis) and 2 units down (negative direction along the y-axis). Let that point be (5, -8).
Connect the two points with a straight line. This line represents the graph of the equation y = -2/5x - 6, which should clearly show a line with a downward trend as it moves to the right.