Question

what is the equation of the trend line in the scatter plot?
use the two orange points to write the equation in slope - intercept form. write any coefficients as integers, proper fractions, or improper fractions in simplest form.

Explanation:

Step1: Identify the two orange points

From the scatter plot, the two orange points are \((3, 7)\) and \((6, 1)\).

Step2: Calculate the slope (\(m\))

The formula for slope is \(m=\frac{y_2 - y_1}{x_2 - x_1}\). Let \((x_1,y_1)=(3,7)\) and \((x_2,y_2)=(6,1)\). Then \(m=\frac{1 - 7}{6 - 3}=\frac{-6}{3}=-2\).

Step3: Find the y-intercept (\(b\))

Use the slope-intercept form \(y = mx + b\) and one of the points, say \((3,7)\). Substitute \(m=-2\), \(x = 3\), and \(y = 7\) into the equation:
\(7=-2(3)+b\)
\(7=-6 + b\)
Add 6 to both sides: \(b=7 + 6=13\)? Wait, no, wait. Wait, let's check the points again. Wait, maybe I mixed up the points. Wait, the orange points: looking at the graph, when \(x = 3\), \(y = 7\); when \(x = 6\), \(y = 1\). Wait, let's recalculate slope: \(\frac{1 - 7}{6 - 3}=\frac{-6}{3}=-2\). Then using point \((3,7)\): \(y=-2x + b\), so \(7=-2(3)+b\) → \(7=-6 + b\) → \(b = 13\)? Wait, that can't be right. Wait, maybe the points are \((3,7)\) and \((6,1)\). Wait, let's check the graph again. Wait, the x-axis: 3, 6. y-axis: 7, 1. Wait, maybe I made a mistake in the points. Wait, no, the orange points: one at (3,7), one at (6,1). Then slope is (1-7)/(6-3)= -6/3= -2. Then using point (6,1): \(y=-2x + b\), so \(1=-2(6)+b\) → \(1=-12 + b\) → \(b = 13\)? Wait, that seems off. Wait, maybe the points are (3,7) and (6,1). Wait, let's plot mentally: when x=3, y=7; x=6, y=1. So the line goes from (3,7) to (6,1). The change in y is -6, change in x is +3, so slope is -2. Then the equation is \(y=-2x + b\). Let's use (3,7): 7 = -23 + b → 7 = -6 + b → b = 13. Wait, but when x=6, y=-26 +13= -12 +13=1, which matches. So the equation is \(y=-2x +13\)? Wait, but let's check with the graph. Wait, maybe I misread the points. Wait, maybe the x-coordinate of the second point is 6, y=1. Yes. So the slope is -2, y-intercept is 13. Wait, but let's check another way. Wait, maybe the points are (3,7) and (6,1). So the equation is \(y=-2x +13\). Wait, but let's see: when x=0, y=13, which is above the graph, but the line is going from (3,7) to (6,1), so that's correct. Wait, maybe that's right.

Answer:

\(y = -2x + 13\)