Graph the equation and identify the y-intercept.
y= _1_
3 x
That equation is not understandable
If the equation is y=1/(3*x), then there is no y-intercept, as the graph approaches the y-axis asymptotically towards -ve and +ve infinity.
To graph the equation y = 1/(3x), we can follow these steps:
1. Choose a range of x-values: Select a few values for x to plot on the graph. It's usually a good idea to include negative and positive values to see the behavior of the function in different regions. Let's choose x = -3, -2, -1, 0, 1, 2, 3.
2. Calculate the corresponding y-values: Plug each x-value into the equation y = 1/(3x) and calculate the corresponding y-value.
For example, when x = -3:
y = 1/(3 * (-3)) = -1/9
3. Plot the points: On a coordinate plane, plot each point (x, y) using the calculated values from step 2.
The coordinates for the chosen x-values would be as follows:
(-3, -1/9), (-2, -1/6), (-1, -1/3), (0, undefined), (1, 1/3), (2, 1/6), (3, 1/9)
Note: The y-value is undefined when x = 0 because division by zero is not possible.
4. Draw the graph: Connect the plotted points with a smooth curve. Since the equation is y = 1/(3x), the graph will be a hyperbola.
To identify the y-intercept, we can look at the point where the graph intersects the y-axis. In other words, we need to find the value of y when x = 0.
Using the equation y = 1/(3x), when x = 0, the equation becomes y = 1/(3 * 0) = undefined.
Therefore, there is no y-intercept for this equation.