Final answer:
To graph y = -3x + 4, plot the y-intercept (0, 4) first and then use the slope -3 to find the next point by moving right 1 unit and down 3 units to (1, 1). Connect these points with a line to graph the equation.
Step-by-step explanation:
To graph the equation y = -3x + 4, start by plotting the y-intercept, which is the point at which the line will cross the y-axis. In this case, the y-intercept is 4, so you would place your first point at (0, 4) on the graph. This point corresponds to where x is 0.
Next, use the slope to determine the second point. The slope of the line is -3, which tells you that for every 1 unit increase in x, y will decrease by 3 units. From your first point, move right 1 unit on the x-axis and then down 3 units on the y-axis to find the second point at (1, 1). Plot this second point. Connecting these two points with a straight line gives you the graph of the equation.
If you need to plot additional points to confirm the linearity, simply continue using the slope: move right another unit on the x-axis and down another 3 units on the y-axis, and plot each new point. Once you have all the points plotted, draw a line through them to complete the graph of the equation.