To determine the correct formula for the function based on the options you've provided, we'll need to analyze the slope and y-intercept of the graph of each equation.
General Form of Linear Equation
The general form of a linear equation is \(y = mx + b\) where:
- \(m\) is the slope of the line.
- \(b\) is the y-intercept (the value of \(y\) when \(x = 0\)).
Analyzing Each Option
-
y = –3x – 1
- Slope (m): -3
- Y-Intercept (b): -1
-
y = 3x + 1
- Slope (m): 3
- Y-Intercept (b): +1
-
y = –3x + 1
- Slope (m): -3
- Y-Intercept (b): +1
-
y = 3x – 1
- Slope (m): 3
- Y-Intercept (b): -1
Steps to Identify the Correct Equation
-
Identify the slope: Check if the line is increasing or decreasing. If it goes up from left to right, the slope is positive (options with +3). If it goes down, the slope is negative (options with -3).
-
Identify the y-intercept: Look at where the line crosses the y-axis.
Conclusion
Without the graphical representation, I'm unable to define the characteristics of the line directly. However, if you can provide the slope (increasing or decreasing) and the y-intercept from the graph, I can assist in confirming which equation matches the function displayed.
- If the slope is negative and the line crosses the y-axis at -1, choose \(y = –3x – 1\).
- If the slope is negative and it crosses at +1, choose \(y = –3x + 1\).
- If the slope is positive and it crosses at +1, choose \(y = 3x + 1\).
- If the slope is positive and it crosses at -1, choose \(y = 3x - 1\).
Please provide further information from the graph if available!
1 answer