How can you come up with the equation of the line of best fit without this applet?

We need two "good" points – points that cross the grid lines. Can you come up with some good points?

For this interactive activity, assistance may be required. Scroll over (tap screen for mobile devices) to see "good" points.

Knowing the coordinates of two points will determine the equation of the line. Pick any two points. I think (14, 350) and (18, 400) are the best points.

midpoint formula: the sum of x sub 1 and x sub 2 divided by 2, the sum of y sub 1 y sub 2 divided by 2; distance formula: the square root of the difference of x sub 2 minus x sub 1 quantity squared plus the difference of y sub 2 minus y sub 2 quantity squared; slop of a line formula: the difference of y sub 2 minus y sub 1 divided by the difference of x sub 2 minus x sub 1

Use the slope of a line formula to find the slope (m).

(14, 350) (18, 400)
(x1, y1) (x2, y2)

m = y sub 2 minus y sub 1 over x sub 2 minus x sub 1 y2 − y1 x2 − x1

m = 400 minus 350 over 18 minus 14 400 − 350 18 − 14

m = 50 over 4 50 4

m = 12.5

Halfway there. There are several ways to proceed. Use point-slope form and convert to slope-intercept form.

Point-slope form: y minus y sub 1 equals m time the difference of x minus x sub 1

The slope is 12.5 and the points we are using are (14, 350) and (18, 400). You can use either point. I will use both to show that either point will produce the same equation.

y − y1 = m( x − x1)

y − 350 = 12.5( x − 14)

y − 350 = 12.5x − 175

 + 350              +350

        y = 12.5x + 175

y − y1 = m( x − x1)

y − 400 = 12.5( x − 18)

y − 350 = 12.5x − 225

 + 400              +400

        y = 12.5x + 175

The equation is now in slope-intercept form.

The slope is the rate of change in the data. Using the axes, the rate of change is in calories per gram of fat (c/g). From the slope we know the food is following a pattern of increasing 12.5 calories for every gram of fat added.

The intercept is the y-intercept. In this case, the y-intercept of (0, 175) means a sandwich with 0 grams of fat would have 175 calories.