Question

passing statistics
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?
$y = 3x + 79$
$y = 3x + 55$
$y = 3x + 65$
$y = 3x + 31$

Explanation:

Step1: Recall the slope - intercept form

The equation of a line in slope - intercept form is \(y = mx + b\), where \(m\) is the slope and \(b\) is the \(y\) - intercept. We know \(m = 3\), so the equation is \(y=3x + b\).

Step2: Substitute a point into the equation

We can use the point \((x = 24,y = 127)\). Substitute into \(y = 3x + b\):
\(127=3\times24 + b\)
\(127 = 72 + b\)

Step3: Solve for \(b\)

Subtract 72 from both sides:
\(b=127 - 72\)
\(b = 55\)

Answer:

\(y = 3x+55\)