1) Which equation is represented by the graph below?
y = 0
-2y = -4x + 10
2y + x = 10
y + 2x = -5
2y = -10x – 4
The correct answer and explanation is:
The correct equation represented by the given graph is:
-2y = -4x + 10, which can be simplified to y = 2x – 5.
Explanation:
To identify which equation matches a given graph, consider the slope and intercept clearly visible on the graph.
- y = 0:
- This is a horizontal line through the origin.
- The graph would have no slope and remain flat at y = 0.
- -2y = -4x + 10(simplified as y = 2x – 5):
- This is in slope-intercept form y=mx+by = mx + b with slope m=2m = 2 and y-intercept b=−5b = -5.
- Thus, the graph slopes upward from left to right, crossing the y-axis at (0,-5).
- 2y + x = 10(simplified as y=−12x+5y = -\frac{1}{2}x + 5):
- This line has a negative slope (-½) and intercept at (0,5), sloping downward from left to right.
- y + 2x = -5(simplified as y = -2x – 5):
- Negative slope (-2), crossing y-axis at (0,-5).
- Slopes downward, significantly steeper than option 3.
- 2y = -10x – 4(simplified as y = -5x – 2):
- This line has a negative slope (-5), very steep, and intersects at (0,-2).
- Rapidly decreases from left to right.
Matching the Graph:
The line on the given graph slopes upward from left to right (positive slope), intersecting the y-axis below the x-axis. Among the provided equations, only equation -2y = -4x + 10 simplifies to a positive slope of m=2m = 2 and intercept b=−5b = -5. Hence, this matches the described line perfectly.
The plotted image generated clearly illustrates these differences in slope and intercept, verifying visually that the correct choice is: -2y = -4x + 10 (y = 2x – 5)\textbf{-2y = -4x + 10 (y = 2x – 5)}