Which graph shows the line Y = -3x + 1 Question 9 of 42: Which graph shows the line y = -3x + 1? Graph B B. Graph A Graph C Graph D 6 PREVIOUS Scan Boi
The Correct Answer and Explanation is:
Explanation:
To identify the correct graph for the linear equation y = -3x + 1, one can analyze its two key components based on the slope-intercept form, y = mx + b.
- The Y-Intercept (b): In the equation y = -3x + 1, the value of ‘b’ is +1. This tells you the point where the line crosses the vertical y-axis. Therefore, the correct graph must pass through the point (0, 1). Looking at the four lines provided:
- Graph A and Graph C cross the y-axis at (0, -1). They are incorrect.
- Graph B and Graph D both cross the y-axis at (0, 1). One of these must be the correct answer.
- **The Slope slopes (they go up from left to right).
This eliminates Graphs A and C.
3. Combine the findings:
The correct graph must have a y-intercept of +1 and a negative slope. The only line that meets both these requirements is Graph B.
To further confirm, you can check the slope value of -3 on Graph B. The slope -3 can be thought of as “rise over run,” or -3/1. This means from any point on (m):** In the equation y = -3x + 1, the slope ‘m’ is -3. The slope indicates the steepness and direction of the line. A slope of -3 can be written as the fraction -3/1. This means for every 1 unit you move to the right on the graph (the “run”), you must the line, if you move 1 unit to the right, you must move 3 units down.
- Start at the y-intercept of Graph B, which is (0, 1).
- Move 1 unit to the right (to x = 1).
- Move 3 units down (from y = 1 to y = -2).
- This lands you on the point (1, -2), which is exactly on Graph B.
Therefore, Graph B correctly represents the line y = -3x + 1. The correct option is A. move 3 units down (the “rise,” which is negative in this case).
* Let's test this on the remaining options, Graph B and Graph D, starting from their y-intercept at (0, 1).
* **For Graph B (the green line):** Starting at (0, 1), if you move 1 unit to the right to x=1 and 3 units down to y=-2, you land on the