The equation y = 3x + 6 represents a linear function where the graph is a straight line.
To graph this equation, we can start by identifying two key characteristics: the slope and the y-intercept. In the equation, the number next to x (which is 3) is the slope. This means that for every unit increase in x, the value of y increases by 3 units. The number 6 is the y-intercept, which is the point where the line crosses the y-axis. This occurs when x is 0. So, at x = 0, y = 6.
To plot the graph, we can find a couple of points:
- When x = 0:
y = 3(0) + 6 = 6.
So one point is (0, 6). - When x = 1:
y = 3(1) + 6 = 9.
So another point is (1, 9).
Plotting these two points on a graph and drawing a line through them will give us the representation of the function. The line will extend infinitely in both directions, illustrating that the relationship expressed by y = 3x + 6 holds for all values of x.