Question

Couples are marrying later. The median age of men who tied the knot for the first time in 1970 was 23.2. In 1998, the median age was 26.7. Write an equation, in slopeintercept form to predict the median age that men marry M for any year t.

Answer 1

Answer:

$M = \frac{1}{8}t -223. 05$

Step-by-step explanation:

The slope-intercept form of the equation of a line is:

$y = mx + b$

Where m is the slope of the line and b is the intercept with the y axis.

$m = \frac{y_2-y_1}{x_2-x_1}\\\\m = \frac{26.7-23.2}{1998 - 1970}\\\\m = \frac{1}{8}$

So:

$y = \frac{1}{8}x + b$

To find b we take the point (1970, 23.2) and introduce it in the previous equation.

$23.2 = \frac{1}{8}(1970) + b\\\\23.2 - 246.25 = b\\\\b = -223. 05$

Then the equation is:

$M = \frac{1}{8}t -223. 05$