Question

Liz and Sara are making cookies for a bake sale. The graph shows the number of cookies that Liz bakes during a 5-hour period. Graph in the coordinate plane with title cookies baked by Liz. Vertical axis goes from 0 to 220 in increments of 10 and is labeled number of cookies baked. Horizontal axis goes from 0 to 5 in increments of 1 and is labeled time in hours. A ray on the graph starts at point begin ordered pair 0 comma 19 end ordered pair and goes through point begin ordered pair 4 comma 179 end ordered pair. The equation y = 45x + 38 shows the number of cookies that Sara bakes during the same hours with y representing the number of cookies and x representing the number of hours. Which statements about the cookie baking by the two girls are true? Select each correct answer. Sara had baked more cookies at the start of the 5 hours than Liz.

Liz bakes more cookies each hour than Sara.
Liz bakes 19 cookies each hour.
Sara bakes 45 cookies each hour.

Answer 1

The given option A and D are correct

Explanation:

Given: The equation y = 45x+38 shows the Sara bakes during the same hours. ; where y is the number of cookies and x is the number of hours. ......[1]

Option A :

It is given from the graph that at the start of the 5 hours

Liz has baked 220 cookies.

To find the number of cookies that Sara has baked for 5 hours.

Substitute the value of x =5 in [1];

`y = 45 * 5 +38 = 225 +38 = 263`

Sara has baked 263 cookies in 5 hours,

therefore, we have;

Therefore, sara had baked more cookies at the start of the 5 hours than Liz.

Hence the option A is correct.

Option C

For Liz

First find the slope:

here, slope represents the cookies baked each hour.

It is given by :
`m = (y_2-y_1)/(x_2-x_1)` where m is the slope.

From the graph we have the points (0, 19) and ( 1, 179)

then, substitute these in the slope formula:

`m = (179-19)/(4-0) =(160)/(4) = 40`

Therefore, the Liz bakes 40 cookies each hour.

Therefore, Option C is incorrect.

Option D

Since, the number of cookies baked each hour is equal to the slope of the linear equation [1]

therefore, slope = 45 cookies/hour

Hence, the Sara bakes 45 cookies each hour.

Therefore, the option D is correct.

Option B

As you can see that

Liz bakes 40 cookies each hour and

Sara bakes 45 cookies each hour

Therefore, the given statement in option B: Liz makes more cookies each hour than Sara is incorrect