Final answer:
The graph of the equation y = -45x - 1 is a straight line with a slope of -45 and a y-intercept of -1.
Explanation:
The given equation, y = -45x - 1, is in slope-intercept form (y = mx + b), where "m" is the slope and "b" is the y-intercept. In this case, the slope is -45, indicating that for every unit increase in x, the y-value decreases by 45 units. The y-intercept is -1, which is the point where the line crosses the y-axis.
To graph the equation, start at the y-intercept (0, -1) and use the slope to find another point on the line. For example, if you move one unit to the right (increase x by 1), you would move down 45 units (decrease y by 45) to reach the next point. Repeat this process to plot several points and then connect them to form a straight line.
The steep slope of -45 indicates a rapid decrease in the y-values as x increases. The line extends infinitely in both directions, representing all possible solutions to the equation. The resulting graph is a downward-sloping line that intersects the y-axis at -1.
In summary, the graph of y = -45x - 1 is a straight line with a steep negative slope and a y-intercept at -1. The line accurately represents the relationship between x and y as defined by the given equation.