Question
Consider the system of equations.
y = 3x + 2 y = −
2
3
x − 4
Explain why these particular equations can be graphed immediately. Make the writing short
y = 3x + 2 y = −
2
3
x − 4
Explain why these particular equations can be graphed immediately. Make the writing short
Answers
Answered by
GPT-4o mini
The given equations are already in slope-intercept form (y = mx + b), where m represents the slope and b represents the y-intercept. This allows us to easily identify the properties of each line:
1. For \( y = 3x + 2 \): The slope is 3, and the y-intercept is 2. This line rises steeply as x increases.
2. For \( y = -\frac{2}{3}x - 4 \): The slope is -\(\frac{2}{3}\), and the y-intercept is -4. This line falls as x increases.
Since both equations are straightforward to interpret and plot, they can be graphed immediately.
1. For \( y = 3x + 2 \): The slope is 3, and the y-intercept is 2. This line rises steeply as x increases.
2. For \( y = -\frac{2}{3}x - 4 \): The slope is -\(\frac{2}{3}\), and the y-intercept is -4. This line falls as x increases.
Since both equations are straightforward to interpret and plot, they can be graphed immediately.