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

From the scatter plot, the two yellow points are at \((0, 40)\) and \((90, 58)\) (wait, looking again, the first yellow point is \((0, 40)\) and the second is \((90, 58)\)? Wait, no, let's check the grid. Wait, the first yellow point: when \(x = 0\), \(y = 40\), so \((0, 40)\). The second yellow point: when \(x = 90\), \(y = 58\)? Wait, no, maybe I misread. Wait, the line goes through \((0, 40)\) and \((90, 58)\)? Wait, no, let's calculate the slope. Wait, maybe the second point is \((90, 58)\)? Wait, no, let's do it properly. Wait, the first point is \((0, 40)\) (since at \(x=0\), \(y=40\)). The second yellow point: looking at the graph, when \(x = 90\), the yellow dot is at \(y = 58\)? Wait, no, maybe the coordinates are \((0, 40)\) and \((90, 58)\)? Wait, no, let's check the difference. Wait, maybe the second point is \((90, 58)\)? Wait, no, let's calculate the slope. The slope \(m\) is \(\frac{y_2 - y_1}{x_2 - x_1}\). Let's take \((0, 40)\) as \((x_1, y_1)\) and \((90, 58)\) as \((x_2, y_2)\). Then \(m=\frac{58 - 40}{90 - 0}=\frac{18}{90}=\frac{1}{5}\). Wait, that makes sense. Wait, 58 - 40 is 18, 90 - 0 is 90, 18/90 is 1/5. Then the y-intercept \(b\) is 40, since when \(x=0\), \(y=40\). So the slope-intercept form is \(y = mx + b\), where \(m=\frac{1}{5}\) and \(b = 40\). Wait, let's check again. Wait, maybe the second point is \((90, 58)\)? Wait, no, maybe I made a mistake. Wait, let's look at the graph again. The first yellow point: \(x=0\), \(y=40\) (so \((0, 40)\)). The second yellow point: \(x=90\), \(y=58\)? Wait, no, 40 to 58 is 18 over 90, which is 1/5. So slope \(m=\frac{1}{5}\), y-intercept \(b = 40\). So the equation is \(y=\frac{1}{5}x + 40\)? Wait, no, wait, maybe the second point is \((90, 58)\)? Wait, no, let's recalculate. Wait, if the two points are \((0, 40)\) and \((90, 58)\), then slope is \(\frac{58 - 40}{90 - 0}=\frac{18}{90}=\frac{1}{5}\). So \(m=\frac{1}{5}\), \(b = 40\). So the equation is \(y=\frac{1}{5}x + 40\). Wait, but let's check with another point. If \(x = 90\), then \(y=\frac{1}{5}(90)+40 = 18 + 40 = 58\), which matches the second yellow point. So that's correct.

Step2: Write the slope-intercept form

The slope-intercept form is \(y = mx + b\), where \(m\) is the slope and \(b\) is the y-intercept. We found \(m=\frac{1}{5}\) and \(b = 40\). So the equation is \(y=\frac{1}{5}x + 40\).

Answer:

\(y = \frac{1}{5}x + 40\)