Question

for the data given below, answer parts (a) through (d)
x: -19, -16, -14, -13, -9
y: 102, 122, 120, 132, 142
y = 3.8613x + 178.4307
(d) use a graphing utility to draw the scatter plot and graph the line of best fit on it
choose the correct graph below. all graphs are shown with a viewing window of -25,0,5×90,198,10.
options: a, b, c, d (with corresponding graphs)
help me solve this view an example get more help

Explanation:

Step1: Analyze the slope of the line of best fit

The equation of the line of best fit is \( y = 3.8613x + 178.4307 \). The slope (\( m = 3.8613 \)) is positive, so the line should be increasing (going up from left to right). This eliminates options A and C (which have negative - sloping lines).

Step2: Analyze the scatter plot points

We have the data points:

• When \( x=-19 \), \( y = 102 \)
• When \( x=-16 \), \( y = 122 \)
• When \( x=-14 \), \( y = 120 \)
• When \( x=-13 \), \( y = 132 \)
• When \( x=-9 \), \( y = 142 \)

As \( x \) increases (becomes less negative), \( y \) generally increases. Let's check the position of the points relative to the line. For a positive - sloped line, as \( x \) increases, \( y \) should increase. Now, let's check the two remaining options (B and D). Option B seems to have points that are more in line with the trend of the positive - sloped line \( y = 3.8613x+178.4307 \). Option D's points seem to be less consistent with the given data points. Also, when we substitute \( x=-19 \) into the line equation: \( y=3.8613\times(-19)+178.4307=-73.3647 + 178.4307 = 105.066 \), which is close to \( y = 102 \). When \( x=-9 \), \( y=3.8613\times(-9)+178.4307=-34.7517+178.4307 = 143.679 \), which is close to \( y = 142 \). The points in option B seem to follow the trend of the line better.

Answer:

B