Final answer:
To solve the system by graphing, convert the equation to slope-intercept form, graph the line using the slope and y-intercept, and note that parallel lines have the same slope.
Step-by-step explanation:
To solve the system by graphing the given equation -2x = 2y - 4, you first need to convert it into slope-intercept form, which is y = mx + b, where m is the slope and b is the y-intercept. You can do this by isolating y in the equation:
First add 2x to both sides to get:
2y = 2x - 4
Then divide everything by 2 to solve for y:
y = x - 2
Now, this is in the slope-intercept form y = b + mx, with a slope (m) of 1 and a y-intercept (b) of -2. To graph this equation, you start at the y-intercept ((0, -2)) on the graph, and then use the slope to find another point. Since the slope is 1, from the y-intercept you would go up 1 unit and right 1 unit to find another point on the line. Connect these two points with a straight line, and you have graphed the equation.
To express equations graphically is not only to draw them on a graph; it also includes understanding the characteristics of the line such as slope and intercepts. In the context of the line of best fit, it's clear that the equations Y2 = -173.5 + 4.83x - 2(16.4), and Y3 = -173.5 + 4.83x + 2(16.4) are parallel to the best-fit line y = -173.5 + 4.83x, because they share the same slope of 4.83 and their y-intercepts are equal distance away from the best-fit line's y-intercept, but in opposite directions due to the subtraction and addition of 2(16.4).