Questions: Which answer choice represents the graph? A) y=2x+4 B) y=-2x+4 C) y=2/3x+4 D) y=-2/3x+4

Which answer choice represents the graph? A) y=2x+4 B) y=-2x+4 C) y=2/3x+4 D) y=-2/3x+4
Transcript text: Which answer choice represents the graph? A) $y=2 x+4$ B) $y=-2 x+4$ C) $y=\frac{2}{3} x+4$ D) $y=-\frac{2}{3} x+4$
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Solution

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Solution Steps

Step 1: Find the y-intercept

The y-intercept is the point where the line crosses the y-axis. In this graph, the line crosses the y-axis at y = 4.

Step 2: Find the slope

The slope is the change in y divided by the change in x. We can take two points on the line, (0, 4) and (3, 1), and calculate the slope.

Slope = (1 - 4) / (3 - 0) = -3 / 3 = -1

Step 3: Write the equation in slope-intercept form

The slope-intercept form of a linear equation is y = mx + b, where m is the slope and b is the y-intercept. In our case, the slope is -1 and the y-intercept is 4. Therefore, the equation of the line is y = -x + 4.

Final Answer: The correct answer is D) y = -x + 4.

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