Question

The table lists the number of members at a local gym for selected years, where year I represents 2002, year 3 represents 2004, and soon.Year* y = number of members2002 1382004 3532006 573802008 720109100Use the ordered pairs (5,73) and (7,80) to find the equation of a line that approximates the data. Express your answer in slope-intercept form. (If necessary, round the slope to the nearest hundredth and the y-intercept to the nearest whole number.)

Answer 1

ANSWER

y = 3.5x + 56

EXPLANATION

The slope of a line passing through points (x1, y1) and (x2, y2) is,

$m=\frac{y_2-y_1_{}}{x_2-x_1}$

And the slope-intercept form of the equation of a line is,

$y=mx+b$

Where m is the slope and b is the y-intercept.

In this problem, we have to use points (5, 73) and (7, 80) to find the equation of the line. First, we can find the slope,

$m=\frac{80-73}{7-5}=\frac{7}{2}$

For now, the equation is,

$y=\frac{7}{2}x+b$

We have to find the y-intercept, by replacing x and y for the coordinates of one of the given points,

$80=\frac{7}{2}\cdot7+b$

And solve for b,

$80=\frac{49}{2}+b$$b=80-\frac{49}{2}=\frac{160-49}{2}=\frac{111}{2}$

The equation is,

$y=\frac{7}{2}x+\frac{111}{2}$

The slope as a decimal is 3.5 and the y-intercept, rounded to the nearest whole number is 56, so the equation is y = 3.5x + 56