Final answer:
The slope of the line y = -4x is -4 and the y-intercept is 0. The graph of this line has a downward slope and passes through the origin.
Step-by-step explanation:
To find the slope and the y-intercept of the line with the equation y = -4x, we can compare it to the slope-intercept form of a linear equation, y = mx + b. In this equation, the coefficient of x (m) represents the slope and the constant term (b) represents the y-intercept.
Therefore, in the given equation y = -4x, the slope is -4 and the y-intercept is 0. We can interpret this as a line that has a downward slope of 4, meaning that for every 1 unit increase in the x-coordinate, the y-coordinate decreases by 4 units. The y-intercept represents the point where the line intersects the y-axis, which in this case is at the origin (0,0).
To sketch the graph, we start by plotting the y-intercept (0,0) and then using the slope to find other points on the line. For example, if we increase the x-coordinate by 1, the y-coordinate will decrease by 4 units, so we can plot the point (1, -4). We can continue this process to find more points on the line and then connect them to create the graph.