Final answer:
To graph the equation y = |x-2| + 4, plot the vertex at (2, 4), choose x-values, plug them into the equation to find y-values, plot those points, and then draw the V-shaped graph accordingly.
Step-by-step explanation:
The student is asking about the graph of the equation y = |x-2| + 4. To graph this equation, you must first understand that it represents a V-shaped absolute value function. The vertex of this function is at the point (2, 4). You can plot this point on the graph first, and then plot additional points by choosing x-values and determining the corresponding y-values using the given equation. Remember that the absolute value creates two branches: one where x-2 is positive (for x > 2) and one where x-2 is negative (for x < 2).
- Plot the vertex (2,4).
- Pick x-values greater than 2 and calculate the corresponding y-values.
- Pick x-values less than 2 and calculate the y-values, keeping in mind that the absolute value will affect the sign inside the absolute value brackets.
- Connect the points to form the two branches of the V.
In cases where you have a set of data points or a line of best fit to plot, you would follow similar steps of plotting the given points or using the slope and y-intercept to plot the line of best fit.