Let's proceed step by step to understand how to graph the given linear equation B(-1) = 2/3X - 3:
1. Identify the equation. The equation is B(-1) = 2/3X - 3.
2. Reshape the equation to the form y = mx + b, where m is the slope and b is the y-intercept. Given that B(-1) = -1, we substitute this into the equation resulting in -1 = 2/3X - 3. By rearranging, we get the equation y = 2/3X + 4.
3. Identify the slope and the y-intercept from the equation y = 2/3*X + 4. The slope (m) is 2/3 and the y-intercept (b) is 4.
4. Plot the y-intercept. Start by plotting the point (0,4) on the graph. This is where our line will cross the y-axis.
5. Use the slope to find the next point. From the y-intercept, the slope (2/3) means that for every 3 units we move to the right (positive direction along x-axis), we need to move 2 units up (positive direction along y-axis).
6. Continue this method and plot several points on your graph to ensure accuracy.
7. Draw a straight line that passes through the identified points. Make sure your line starts at the bottom of your graph and goes all the way to the top (unless the line is horizontal).
8. Label the x and y axes and provide a title for your graph. These could be the 'X' for the x-axis, 'B(-1)' for the y-axis, and 'Graph of the equation B (-1) = 2/3 X -3' for the title.
Following these steps will allow you to graph the equation B(-1) = 2/3X - 3, or in the manipulated form y = 2/3*X + 4. Be sure to include the negative and positive sides of your graph – linear equations extend infinitely in both directions! Remember that the slope of a function is the rate at which y changes per unit change of x, in this case, for every increase of 3 in X, B(-1) will increase by 2. Particular for this function, if you fill X = 0, you find the point where the function intersects the Y-axis, which is at B(-1) = 4.