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An illustration of a scatterplot graph shows x-axis ranging from 0 to 10 in increments of 1 and y-axis ranging from 0 to 50 in increments of 10. Multiple points are plotted around a line that points downward to the right with an arrowhead on the bottom.
The line passes approximately through left parenthesis 0 comma 45 right parenthesis, left parenthesis 2 comma 25 right parenthesis, left parenthesis 3 comma 15 right parenthesis, and left parenthesis 4.5 comma 0 right parenthesis. 13 points are plotted close to the line.

Write an equation in slope-intercept form of the trend line.

(1 point)
y=
Remaining Attempts : 3
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1 answer

To find the equation of the trend line in slope-intercept form (y = mx + b), we first need to determine the slope (m) and the y-intercept (b).

From the points provided:

  1. Point 1: (0, 45)
  2. Point 2: (2, 25)
  3. Point 3: (3, 15)
  4. Point 4: (4.5, 0)

Let's use the first two points to calculate the slope (m).

The slope formula is: \[ m = \frac{y_2 - y_1}{x_2 - x_1} \]

Using the points (2, 25) and (0, 45): \[ m = \frac{25 - 45}{2 - 0} = \frac{-20}{2} = -10 \]

Now that we have the slope (m = -10), we can use one of the points to find the y-intercept (b). We can use the point (0, 45) since it directly gives us the y-intercept.

The equation of the line becomes: \[ y = -10x + b \]

Substituting (0, 45) into the equation to solve for b: \[ 45 = -10(0) + b \implies b = 45 \]

Thus, the equation of the trend line in slope-intercept form is: \[ y = -10x + 45 \]

So, the final answer is:

y = -10x + 45