A graph titled Passing Statistics has pass attempts on the x-axis, and yards on the y-axis. A line goes through points (24, 127) and (36, 163).

The scatterplot and trend line show the correlation between the number of pass attempts a quarterback makes and the number of yards he throws the ball. The line passes through (24, 127) and (36, 163) and has a slope of 3.

What is equation of the trend line?
y = 3x + 79
y = 3x + 55
y = 3x + 65
y = 3x + 31

1 answer

To find the equation of the trend line, we can use the slope-intercept form of a linear equation, which is given by:

\[ y = mx + b \]

where:

  • \( m \) is the slope,
  • \( b \) is the y-intercept.

We know the slope \( m \) is 3. Now, we need to find the y-intercept \( b \). We can use one of the points on the line to find it. Let's use the point (24, 127).

Substituting the values into the equation:

\[ 127 = 3(24) + b \]

Calculating \( 3(24) \):

\[ 127 = 72 + b \]

Now, solve for \( b \):

\[ b = 127 - 72 = 55 \]

Now we can write the equation of the trend line:

\[ y = 3x + 55 \]

Thus, the correct answer is:

y = 3x + 55.