A common question in calculus is what would happen to the graph of y=4/x if a constant was not present. In this blog post, we will show that when a=4, the graph shifts horizontally by 4 units and vertically by 1 unit. We will also provide an example for how to use this information to solve problems on tests! The graph of y=x/a shifts horizontally by a units and vertically by b when the constant is not present. In our example, we will use x to represent horizontal movement and a to represent vertical movement. The following sketch shows what would happen if Âa = 16: y-intercept: 0; Slope(or rise): -16/(n+0) or -b/a=-16/-32 or -b*-65/512 which equals about 18.75 in this case; Equation for y-axis intercept: (0,18)/(-16); Corresponding point on the line segment with slope 65 over 512 from (-64,-1024) => (-72,-992). We can use these points to graph the new line: y = -x/a, since a=16. The point (-72,-992) is now (0,18). It’s important to note that in our example of y=-x/(-32), the x values are 32 instead of 0 because we’re solving for what would happen if Âa > 0 and multiplying by a positive number does not change sign. To save time on tests, students should remember this information when graphing! When calculating from one quadrant into another with negative numbers present in both parts of an equation like Y+X = A or X+Y = B where at least one variable is nonnegative then it will be necessary to calculate twice