Suppose you have $30 to spend on bags of tootsie rolls that are worth $3 and bags of lollipops worth $5. if you have to use all of their money, what combinations of candy bags can they buy? construct a linear equation and find/explain the y-intercept, x-intercept, and slope. finally, if you have $45 to spend on the candy, how would that impact everything?

see below

Step-by-step explanation:

Let x = tootsie rolls

y = lollipops

Toosie rolls are 3 dollars and lollipops are $5 and you only have 30 dollars.

3x+5y =30

To find the x intercept, set y=0 and solve for x

3x +0 = 30

3x = 30

Divide by 3

3x/3 = 30/3

x = 10

The x intercept is 10.  This means if you get no lollipops, you can have ten tootsie rolls.

To find the y intercept, set x=0 and solve for y

0 +5y = 30

5y = 30

Divide by 5

5y/5 = 30/5

x = 6

The y intercept is 6.  This means if you get no tootsie rolls you can have 6 lollipops.

To find the slope, solve the equation for y

3x+5y =30

Subtract 3x from each side

3x-3x+5y = -3x+30

5y = -3x+30

Divide by 5

y = -3/5 x +30/5

y = -3/5 x +6

The slope is -3/5.  For every three less lollipops you get, you can have 5 more tootsie rolls.

If you have $45 dollars instead of 30,  this will change the x and y intercepts, but not the slope.  

3x+5y =45

To find the x intercept, set y=0 and solve for x

3x +0 = 45

3x = 45

Divide by 3

3x/3 = 45/3

x = 15

The x intercept is 15.  This means if you get no lollipops, you can have 15 tootsie rolls.

To find the y intercept, set x=0 and solve for y

0 +5y = 45

5y = 45

Divide by 5

5y/5 = 45/5

x = 9

The y intercept is 9.  This means if you get no tootsie rolls you can have 9 lollipops.

To find the slope, solve the equation for y

3x+5y =45

Subtract 3x from each side

3x-3x+5y = -3x+45

5y = -3x+45

Divide by 5

y = -3/5 x +45/5

y = -3/5 x +9

The slope is -3/5.  For every three less lollipops you get, you can have 5 more tootsie rolls.

- "runner b is moving at a slower rate."

- "the graphs shown are graphs of distance(km) against time(min).

the slopes of this graphs are are given by:

slope = (change in y)/(change in x)

= (change in distance)/(change in time)

this is the formula for finding the speed. so, the slope of these graphs represent the speed of the runner.

taking each division in the graph to represent 1 on both axis:

runner a ⇒ speed = (2-0)/(1-0)

= 2/1

= 2 km/min

runner b ⇒ speed = (3-0)/(3-0)

= 3/3

= 1 km/min

this shows that   runner b is moving at a slower rate."