Question

what is the equation of the trend line in the scatter plot?
use the two yellow 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 yellow points

The two yellow points are at \((4, 0)\) and \((8, 9)\).

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

The formula for slope is \(m = \frac{y_2 - y_1}{x_2 - x_1}\). Substituting the points \((4, 0)\) as \((x_1, y_1)\) and \((8, 9)\) as \((x_2, y_2)\), we get:
\(m = \frac{9 - 0}{8 - 4} = \frac{9}{4}\)

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

Using the slope-intercept form \(y = mx + b\) and the point \((4, 0)\):
\(0 = \frac{9}{4}(4) + b\)
\(0 = 9 + b\)
\(b = -9\)

Step4: Write the equation

Substituting \(m = \frac{9}{4}\) and \(b = -9\) into \(y = mx + b\), we get:
\(y = \frac{9}{4}x - 9\)

Wait, that seems incorrect. Let's recheck the points. Wait, looking at the graph, the lower yellow point is at (4, 0)? Wait, no, maybe I misread the coordinates. Wait, the x-axis: the lower yellow point is at x=4, y=0? Wait, no, looking at the grid, when x=4, y=0? Wait, the upper yellow point is at (8, 9)? Wait, no, maybe the lower yellow point is (4, 0) and the upper is (8, 9)? Wait, no, let's check the grid again. Wait, the y-axis: the lower yellow point is at y=0, x=4. The upper yellow point: x=8, y=9? Wait, no, maybe the lower point is (4, 0) and the upper is (8, 9)? Wait, but when we calculate the slope, (9 - 0)/(8 - 4) = 9/4. But let's check with another point. Wait, maybe I made a mistake in the coordinates. Wait, the lower yellow point: x=4, y=0. The upper yellow point: x=8, y=9? Wait, no, looking at the graph, the upper yellow point is at (8, 9)? Wait, the grid lines: each square is 1 unit. So x=4, y=0 (the lower yellow dot) and x=8, y=9 (the upper yellow dot). Wait, but let's check the slope again. Wait, maybe the lower point is (4, 0) and the upper is (8, 9). Then slope is (9-0)/(8-4)=9/4. Then using point (4,0): y = (9/4)x + b. 0 = (9/4)*4 + b => 0 = 9 + b => b = -9. So equation is y = (9/4)x - 9. But that seems odd. Wait, maybe I misread the lower point. Wait, maybe the lower yellow point is (4, 0) and the upper is (8, 9). Wait, but let's check the graph again. Wait, the x-axis: 0,1,2,3,4,5,6,7,8,9,10. The lower yellow dot is at x=4, y=0. The upper yellow dot is at x=8, y=9. Yes. So slope is 9/4, y-intercept is -9. So equation is y = (9/4)x - 9.

Wait, but maybe I made a mistake. Let's check again. Wait, the lower point: x=4, y=0. Upper point: x=8, y=9. So the change in y is 9 - 0 = 9. Change in x is 8 - 4 = 4. So slope is 9/4. Then using y = mx + b, plug in (4,0): 0 = (9/4)(4) + b => 0 = 9 + b => b = -9. So equation is y = (9/4)x - 9.

But wait, maybe the lower point is (4, 0) and the upper is (8, 9). Yes, that seems correct. So the equation is y = (9/4)x - 9.

Wait, no, that can't be right. Wait, maybe the lower point is (4, 0) and the upper is (8, 9). Wait, but when x=4, y=0: 0 = (9/4)4 - 9 => 0 = 9 - 9 => 0=0. Correct. When x=8, y=(9/4)8 -9 = 18 -9 =9. Correct. So that's the equation.

Answer:

\(y = \frac{9}{4}x - 9\)