To graph the linear equation y=4/5x, plot the y-intercept at the origin, use the slope to plot additional points, and then draw a straight line through these points. The slope indicates the rate at which y increases for a given increase in x, reflecting the dependence of y on x.
To graph y=4/5x on a coordinate plane, you should first understand the dependence of y on x. This equation represents a linear relationship between x and y, where y changes as a function of x. The slope (rise over run) of the line is 4/5, which means for each increase of 5 units in x, y increases by 4 units.
Begin by plotting the y-intercept, which is the point where the line crosses the y-axis. In this case, the y-intercept is 0, since there is no constant added to 4/5x. Next, use the slope to plot other points. Starting at the origin (0,0), move 5 units to the right (positive x-direction) and 4 units up (positive y-direction) to reach the next point (5, 4). Repeat this process to find more points if necessary.
You can then draw a straight line through these points, extending it in both directions. Make sure to label the axes with 'x' for the horizontal axis and 'f(x)' or 'y' for the vertical axis. Scale the axes appropriately to include the points you have plotted. Lastly, review your graph to ensure it is a straight line with a slope of 4/5, reflecting the linear dependence of y on x.