Ask a New Question
Menu

Use the image to answer the question.

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=
x +
Remaining Attempts : 3

1 answer

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

The points that the line passes through approximately are:

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

First, let's calculate the slope \(m\) using two points, say (0, 45) and (4.5, 0).

The formula for the slope \(m\) between two points \((x_1, y_1)\) and \((x_2, y_2)\) is: \[ m = \frac{y_2 - y_1}{x_2 - x_1} \]

Using (0, 45) as \((x_1, y_1)\) and (4.5, 0) as \((x_2, y_2)\): \[ m = \frac{0 - 45}{4.5 - 0} = \frac{-45}{4.5} = -10 \]

Now that we have the slope, we can use one of the points to find the y-intercept \(b\). Using the point (0, 45): \[ y = mx + b \] Substitute \(m = -10\) and the coordinates of the point (0, 45): \[ 45 = -10(0) + b \] \[ b = 45 \]

Now we have both the slope and the y-intercept:

  • Slope \(m = -10\)
  • Y-intercept \(b = 45\)

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

So the answer is: \[ y = -10x + 45 \]