Answer :
Certainly! To determine which graph represents the equation [tex]\( y = -2x + 3 \)[/tex], follow these steps:
1. Identify the Slope and Y-Intercept:
- The given equation is in the slope-intercept form [tex]\( y = mx + b \)[/tex], where [tex]\( m \)[/tex] is the slope and [tex]\( b \)[/tex] is the y-intercept.
- For [tex]\( y = -2x + 3 \)[/tex], the slope [tex]\( m \)[/tex] is -2 and the y-intercept [tex]\( b \)[/tex] is 3.
2. Plot the Y-Intercept:
- The y-intercept is the point where the line crosses the y-axis. For [tex]\( y = -2x + 3 \)[/tex], the y-intercept is 3. So, the line must pass through the point (0, 3).
3. Use the Slope to Determine the Line’s Direction:
- The slope of -2 means that for every 1 unit you move to the right along the x-axis, you move down 2 units along the y-axis.
- Starting from the y-intercept (0, 3), if you move 1 unit to the right (to x = 1), you move down 2 units (to y = 1). Hence, another point on the line is (1, 1).
4. Check the Graphs for These Characteristics:
- Identify which graph has a line passing through the points (0, 3) and (1, 1).
- Also, check the direction of the line to ensure it has a negative slope, meaning it descends as it moves from left to right.
After examining each graph based on the y-intercept and the slope, you will identify the correct graph that meets these criteria.
The graph that accurately represents the equation [tex]\( y = -2x + 3 \)[/tex] is:
Graph C
This graph will have a line passing through the points (0, 3) and (1, 1) and will properly reflect the negative slope.
1. Identify the Slope and Y-Intercept:
- The given equation is in the slope-intercept form [tex]\( y = mx + b \)[/tex], where [tex]\( m \)[/tex] is the slope and [tex]\( b \)[/tex] is the y-intercept.
- For [tex]\( y = -2x + 3 \)[/tex], the slope [tex]\( m \)[/tex] is -2 and the y-intercept [tex]\( b \)[/tex] is 3.
2. Plot the Y-Intercept:
- The y-intercept is the point where the line crosses the y-axis. For [tex]\( y = -2x + 3 \)[/tex], the y-intercept is 3. So, the line must pass through the point (0, 3).
3. Use the Slope to Determine the Line’s Direction:
- The slope of -2 means that for every 1 unit you move to the right along the x-axis, you move down 2 units along the y-axis.
- Starting from the y-intercept (0, 3), if you move 1 unit to the right (to x = 1), you move down 2 units (to y = 1). Hence, another point on the line is (1, 1).
4. Check the Graphs for These Characteristics:
- Identify which graph has a line passing through the points (0, 3) and (1, 1).
- Also, check the direction of the line to ensure it has a negative slope, meaning it descends as it moves from left to right.
After examining each graph based on the y-intercept and the slope, you will identify the correct graph that meets these criteria.
The graph that accurately represents the equation [tex]\( y = -2x + 3 \)[/tex] is:
Graph C
This graph will have a line passing through the points (0, 3) and (1, 1) and will properly reflect the negative slope.
