Final Answer:
The equation y = 2x + 47 represents a straight line on a Cartesian plane.
Step-by-step explanation:
The equation y = 2x + 47 is in slope-intercept form (y = mx + b), where 'm' represents the slope of the line, and 'b' is the y-intercept. Here, the slope is 2, indicating that for every unit increase in x, y will increase by 2. The y-intercept, which is the point where the line intersects the y-axis, is 47. This means that when x is 0, y equals 47, positioning the line above the y-axis at y = 47.
To graph this equation, start by plotting the y-intercept at (0, 47). Then, using the slope, determine another point on the line. Since the slope is 2, for every increase of 1 in x, y increases by 2. Thus, from the y-intercept (0, 47), move one unit to the right and two units up to locate another point. Connect these two points, and you'll have the graph of y = 2x + 47, a straight line extending infinitely in both directions.
This line will have a positive slope, rising at a constant rate as x increases. Conversely, as x decreases, y will decrease following the same rate. The graphical representation illustrates the relationship between x and y values described by the equation, providing a visual understanding of how changes in x affect y based on the equation's parameters.