Question

select which slope is suitable for this line?
options: 4/3, 2/3, 0

Explanation:

Step1: Recall Slope Formula

The slope \( m \) of a line is calculated as \( m=\frac{\Delta y}{\Delta x}=\frac{y_2 - y_1}{x_2 - x_1} \), where \( (x_1,y_1) \) and \( (x_2,y_2) \) are two points on the line.

Step2: Analyze the Line's Trend

The line is increasing (positive slope) and has a gentle rise. Let's pick two points. From the graph, when \( x = 0 \), \( y=- 3 \) (approximate), and when \( x = 3 \), \( y=-1 \) (approximate). Then \( \Delta y=-1-(-3) = 2 \), \( \Delta x=3 - 0=3 \)? Wait, no, maybe better points. Wait, looking at the options, \( 2/3\) or \( 2/1\) or \( 0\)? Wait, the line is increasing, so slope is positive. Let's check the rise over run. If we take two points, say when \( x = 0 \), \( y=-3 \) and \( x = 3 \), \( y=-1 \), then \( \frac{\Delta y}{\Delta x}=\frac{-1 - (-3)}{3-0}=\frac{2}{3}\). Or another pair: when \( x = 3 \), \( y=-1 \) and \( x = 6 \), \( y = 1 \), then \( \frac{1-(-1)}{6 - 3}=\frac{2}{3}\). So the slope should be \( 2/3\)? Wait, the options: first option maybe \( 2/3\), second \( 2/1\), third \( 0 \). Wait, the line is not steep, so \( 2/3\) is more suitable than \( 2/1\) (which is steeper) and \( 0 \) (horizontal). So the suitable slope is \( 2/3\) (assuming the first option is \( 2/3\)).

Answer:

Assuming the first option is \( \boldsymbol{2/3}\), the suitable slope is \( 2/3\). (If the options are: A. \( 2/3\), B. \( 2/1\), C. \( 0 \), then the answer is A. \( 2/3\))