Questions: Which equation matches the graph? a) y=-2x+4 b) y=1/3x-2 c) y=1/2x+2 d) y=-1/2x+2

Which equation matches the graph? a) y=-2x+4 b) y=1/3x-2 c) y=1/2x+2 d) y=-1/2x+2
Transcript text: Which equation matches the graph? a) $y=-2 x+4$ b) $y=\frac{1}{3} x-2$ c) $y=\frac{1}{2} x+2$ d) $y=-\frac{1}{2} x+2$
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Solution

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Solution Steps

Step 1: Identify the y-intercept

The y-intercept is the point where the line crosses the y-axis. From the graph, the line crosses the y-axis at \( y = 2 \).

Step 2: Determine the slope

The slope (m) is the rise over run. From the graph, we can see that as \( x \) increases by 2 units (from 0 to 2), \( y \) decreases by 1 unit (from 2 to 1). Therefore, the slope is: \[ m = \frac{\text{rise}}{\text{run}} = \frac{-1}{2} = -\frac{1}{2} \]

Step 3: Match the equation

Using the slope-intercept form \( y = mx + b \), where \( m \) is the slope and \( b \) is the y-intercept, we have: \[ y = -\frac{1}{2}x + 2 \]

Final Answer

The equation that matches the graph is: \[ \boxed{d) \ y = -\frac{1}{2}x + 2} \]

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