One of the two equations listed in each problem matches the graph. Determine which equation is represented by the graph. Explain how you know your answer is correct
6x + 2y = -4
Or
Y = ⅓(x - 9) + 1
To determine which equation is represented by the graph, we can compare the given equation with the equation of the line in slope-intercept form (y = mx + b).
The equation 6x + 2y = -4 can be rearranged to get y = -3x - 2. This equation has a slope of -3 and a y-intercept of -2.
The equation y = ⅓(x - 9) + 1 can be simplified as y = ⅓x - 2 + 1, which further simplifies to y = ⅓x - 1. This equation also has a slope of ⅓ and a y-intercept of -1.
Comparing the two equations, we can see that they have the same slope (both -3 and ⅓ can be written as a fraction -3/1 and ⅓/1), but different y-intercepts (-2 and -1). Therefore, the equation 6x + 2y = -4 is represented by the graph.
We can also verify our answer by substituting some points from the graph into the equation. Let's choose the point (3, -5):
For equation 6x + 2y = -4:
6(3) + 2(-5) = 18 - 10 = 8, not equal to -4
For equation y = ⅓(x - 9) + 1:
⅓(3 - 9) + 1 = ⅓(-6) + 1 = -2 + 1 = -1, equal to -1
Since the point (3, -5) satisfies the equation y = ⅓(x - 9) + 1 but not the equation 6x + 2y = -4, we can conclude that the equation represented by the graph is y = ⅓(x - 9) + 1.