Which equation models the trend line?

A scatterplot with about 20 points plotted in an upward trend along with a line of best fit that begins at the point zero comma 2 and passes through the point 4 comma 7 point 2.
y = –1.3x + 2
y = 1.3x + 2
y = –1.3x – 2
y = 1.3x – 2

1 answer

To determine which equation models the trend line for the given points, we can use the information about the line of best fit.

  1. The line begins at the point (0, 2). This means that when \( x = 0 \), \( y = 2 \). The y-intercept is therefore 2.
  2. The line passes through the point (4, 7.2).

To find the slope of the line, we can use these two points:

  1. Point 1 (0, 2): This means \( y \) intercept \( b = 2 \).
  2. Point 2 (4, 7.2): We can use the formula for slope, which is: \[ \text{slope} = m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{7.2 - 2}{4 - 0} = \frac{5.2}{4} = 1.3 \]

So, the slope \( m = 1.3 \).

  1. Now we can form the equation of the line in slope-intercept form \( y = mx + b \): \[ y = 1.3x + 2 \]

Now that we’ve established that the equation of the trend line is \( y = 1.3x + 2 \).

Thus, the correct answer is:

y = 1.3x + 2.