Question

select two points on the trend line. (1, __ ) and (8, __ )
use them to find the slope. m = ____
use the slope and the first point from above to write the equation of the trend line. y - __ = (x - __ )
write the trend line in slope - intercept form. y = ____

1. steve drew a trend line for the plotted points. what is steves misunderstanding?

Explanation:

First Problem (Trend Line Equation)

Step1: Identify points on trend line

From the graph, the trend line passes through $(1, 32)$ and $(6, 42)$.

Step2: Calculate the slope

Slope formula: $m=\frac{y_2-y_1}{x_2-x_1}$
$m=\frac{42-32}{6-1}=\frac{10}{5}=2$

Step3: Write point-slope form

Use point $(1,32)$: $y-y_1=m(x-x_1)$
$y-32=2(x-1)$

Step4: Convert to slope-intercept form

Expand and isolate $y$:
$y-32=2x-2$
$y=2x-2+32$
$y=2x+30$

A trend line (line of best fit) should balance the number of points above and below it, representing the overall direction of the data. Steve's line only follows the upper points and does not account for the lower points, so he fails to draw a line that represents the general trend of all the plotted data.

Answer:

$(1, 32)$ and $(6, 42)$
$m=2$
$y-32=2(x-1)$
$y=2x+30$

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Second Problem (Steve's Misunderstanding)