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

y = 3.5x + 56

Step-by-step 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=(80-73)/(7-5)=(7)/(2)`

For now, the equation is,

`y=(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=(7)/(2)\cdot7+b`

And solve for b,

`80=(49)/(2)+b`
`b=80-(49)/(2)=(160-49)/(2)=(111)/(2)`

The equation is,

`y=(7)/(2)x+(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