Which equation represents the graphed function? ?
The Correct Answer and Explanation is:
The correct equation that represents the graphed function is: y=32x−3y = \frac{3}{2}x – 3
This is the third option in the multiple-choice list, and it has been correctly selected in the image.
Explanation
To determine which equation represents the graphed line, we need to identify two key components of a linear equation in slope-intercept form: y=mx+by = mx + b
where:
- mm is the slope (the rate of change or steepness of the line),
- bb is the y-intercept (the point where the line crosses the y-axis).
From the graph, we can observe that the line crosses the y-axis at the point (0,−3)(0, -3). This means the y-intercept, bb, is -3.
Next, we determine the slope. Choose two points that the line passes through. From the graph:
- Point A: (0,−3)(0, -3)
- Point B: (2,0)(2, 0)
To calculate the slope mm, use the formula: m=y2−y1x2−x1m = \frac{y_2 – y_1}{x_2 – x_1}
Using the two points: m=0−(−3)2−0=32m = \frac{0 – (-3)}{2 – 0} = \frac{3}{2}
So the slope m=32m = \frac{3}{2}, and the y-intercept b=−3b = -3.
Putting this into slope-intercept form: y=32x−3y = \frac{3}{2}x – 3
Now, compare this equation with the options given:
- Option A: −3x+2=y-3x + 2 = y → wrong slope and intercept
- Option B: −23x+2=y-\frac{2}{3}x + 2 = y → wrong slope and intercept
- ✅ Option C: 32x−3=y\frac{3}{2}x – 3 = y → correct
- Option D: 2x−3=y2x – 3 = y → wrong slope
Therefore, the correct and best match is: y=32x−3\boxed{y = \frac{3}{2}x – 3}
