Graph the equation using the slope and the y-intercept
y-4/3 x +4
To graph the equation y - 4/3x + 4, we need to determine the slope and y-intercept. The equation is in slope-intercept form (y = mx + b), where M represents the slope and b represents the y-intercept.
The given equation is y - 4/3x + 4, where the coefficient of x is -4/3. To find the slope, we can rewrite the equation in slope-intercept form by solving for y.
y - 4/3x + 4 = 0
Move the -4/3x term to the other side by adding 4/3x to both sides.
y = 4/3x - 4
Now we can see that the slope (m) is 4/3.
Next, let's determine the y-intercept (b), which is the point on the graph where the line intersects with the y-axis. In our equation, the constant term is 4, so the y-intercept is (0, 4).
Now that we have the slope (4/3) and the y-intercept (0, 4), we can proceed to graph the equation.
1. Plot the y-intercept: Start by plotting the point (0, 4) on the graph. This point represents the intersection of the line with the y-axis.
2. Use the slope to find additional points: Since the slope is 4/3, it means for every increase of 1 unit in the x-coordinate, there is an increase of 4/3 units in the y-coordinate. Similarly, for every decrease of 1 unit in the x-coordinate, there is a decrease of 4/3 units in the y-coordinate.
Knowing this, you can choose additional x-values and use the slope to find their respective y-values. For example, if you choose x = 3, the increase would be (1 * 4/3) = 4/3. So, starting from the y-intercept (0, 4), move up 4/3 units. This gives you the second point (3, 4 + 4/3) = (3, 16/3).
3. Connect the points: Once you have enough points, use a straight edge or ruler to draw a line that connects all the plotted points. This line represents the graph of the equation y - 4/3x + 4.
Keep in mind that in graphing linear equations, it is helpful to have at least two points so that you can verify the line is correct and not just a coincidence.