Question

scatter plots: line of best fit write the slope-intercept form equation of the trend line of each scatter plot. ① equation of the trend line: ② equation of the trend line: ③ equation of the trend line:

Explanation:

Problem ①

Step1: Identify two points on the trend line

From the graph, we can see that the trend line passes through \((0, 9)\) (y - intercept) and \((10, 3)\).

Step2: Calculate the slope \(m\)

The formula for slope is \(m=\frac{y_2 - y_1}{x_2 - x_1}\). Let \((x_1,y_1)=(0,9)\) and \((x_2,y_2)=(10,3)\). Then \(m=\frac{3 - 9}{10 - 0}=\frac{-6}{10}=-\frac{3}{5}\).

Step3: Write the equation in slope - intercept form \(y = mx + b\)

We know that the y - intercept \(b = 9\) (from the point \((0,9)\)) and \(m=-\frac{3}{5}\). So the equation is \(y=-\frac{3}{5}x + 9\).

Problem ②

Step1: Identify two points on the trend line

From the graph, the trend line passes through \((0, 10)\) (y - intercept) and \((9, 0)\).

Step2: Calculate the slope \(m\)

Using the slope formula \(m=\frac{y_2 - y_1}{x_2 - x_1}\), with \((x_1,y_1)=(0,10)\) and \((x_2,y_2)=(9,0)\), we get \(m=\frac{0 - 10}{9 - 0}=-\frac{10}{9}\).

Step3: Write the equation in slope - intercept form \(y = mx + b\)

The y - intercept \(b = 10\) (from the point \((0,10)\)) and \(m =-\frac{10}{9}\). So the equation is \(y=-\frac{10}{9}x + 10\).

Problem ③

Step1: Identify two points on the trend line

From the graph, the trend line passes through \((0, 0)\) (y - intercept) and \((25, - 25)\) (approximate, we can also use other points).

Step2: Calculate the slope \(m\)

Using the slope formula \(m=\frac{y_2 - y_1}{x_2 - x_1}\), with \((x_1,y_1)=(0,0)\) and \((x_2,y_2)=(25,-25)\), we get \(m=\frac{-25 - 0}{25 - 0}=- 1\).

Step3: Write the equation in slope - intercept form \(y = mx + b\)

The y - intercept \(b = 0\) (from the point \((0,0)\)) and \(m=-1\). So the equation is \(y=-x+0\) or \(y=-x\).

Answer:

s:

1. \(y =-\frac{3}{5}x + 9\)
2. \(y=-\frac{10}{9}x + 10\)
3. \(y=-x\)