Bill began his diet when he weighed 268 pounds. After 4 weeks he weighed 250 pounds. Write an equation in slope-intercept form o

Question

3 years ago

6

f the line if w represents weeks and p represents pounds

1 answer:

Alika [10] · Answer 1 · 2022-06-04T18:15:30+03:00

An equation in slope-intercept form of the line

$p=-\frac{9}{2}w+268\\$

Given :

Bill began his diet when he weighed 268 pounds.

After 4 weeks he weighed 250 pounds

Lets 'w' represents weeks and 'p' represents pounds

Using the given information ,we find two points (w,p)

Bill began his diet when he weighed 268 pounds.

when w=0 , weight in pounds =268

(0,268)

After 4 weeks he weighed 250 pounds, so point is (4,250)

Use two points to write the equation of line

Slope intercept form is y=mx+b

where m is the slope and b is the y intercept

slope formula using 2 points (0,268) and (4,250)

$m=\frac{y_2-y_1}{x_2-x_1} =\frac{250-268}{4-0} =-\frac{9}{2}$

now use slope m and any one point (0,268) to write equation

$y=mx+b\\y=-\frac{9}{2}x+b\\(0,268) where x=0 and y=268\\268=-\frac{9}{2}(0)+b\\\\b=268$

we know that w represents weeks and p represents pounds

The equation of the line in slope intercept form is

$p=-\frac{9}{2}w+268\\$