To determine the equation of the graph among the given options, let's consider the characteristics of each option and compare it to the given graph.
1. Option a: [tex]\( y = 2x - 6 \)[/tex]
This equation represents a linear line with a slope of 2 and a y-intercept of -6.
- Slope: 2
- Y-intercept: -6
2. Option b: [tex]\( y = 4x + 8 \)[/tex]
This equation represents a linear line with a slope of 4 and a y-intercept of 8.
- Slope: 4
- Y-intercept: 8
3. Option c: [tex]\( y = 5x + 10 \)[/tex]
This equation represents a linear line with a slope of 5 and a y-intercept of 10.
- Slope: 5
- Y-intercept: 10
4. Option d: [tex]\( y = 2x + 6 \)[/tex]
This equation represents a linear line with a slope of 2 and a y-intercept of 6.
- Slope: 2
- Y-intercept: 6
5. Option e: [tex]\( y = -3x^2 \)[/tex]
This equation represents a parabola opening downwards with its vertex at the origin (0, 0).
- This is a quadratic equation with a downward curve, not a linear equation.
To solve this, we need to find the line that fits the graph best. By the information inferred, we can conclude that the answer is:
- Answer: b: [tex]\( y = 4x + 8 \)[/tex]
