We are given a graph that shows the amount of money the Rockwell family budgets for food each month.

We are asked to write an equation to find the total amount of money budgeted in any number of months. First, notice that on the given graph,

y -

axis represents the budgeted amount of money and the

x -

axis represents the number of months.

y x \leftarrow Budgeted amount of money \leftarrow Number of months

We will try to write an equation relating these variables in slope-intercept form.

y = m x + b

In this equation,

m

is the rate of change and

b

is the

y -

intercept. We will first find the rate if change

m .

To do that, we need to know coordinates of two points from the given graph.

We can see that one of the points has the coordinates

x_{1} = 1

and

y_{1} = 625 .

Another point has the coordinates

x_{2} = 2

and

y_{2} = 1250 .

Let's substitute their coordinates into the formula for the rate of change

m .

m = \frac{y _{2} - y _{1}}{x _{2} - x _{1}}

SubstituteValues

Substitute values

m = \frac{1 2 5 0 - 6 2 5}{2 - 1}

SubTerms

Subtract terms

m = \frac{6 2 5}{1}

DivByOne

$\frac{a}{1} = a$

m = 625

We found that the rate of change is equal to

625 .

This means that the Rockwell family budgets

625

dollars per month for food. Now let's substitute

m = 625

into the equation in slope-intercept form.

y = m x + b ⇕ y = 625 x + b

To find the

y -

intercept

b,

we can substitute any point from the graph into this equation and solve for

b .

Let's choose the point

(1, 625) .

y = 625 x + b

SubstituteII

$x = 1$ , $y = 625$

625 = 625 (1) + b

▼

Solve for

b

IdPropMult

Identity Property of Multiplication

625 = 625 + b

SubEqn

$LHS - 625 = RHS - 625$

0 = b

RearrangeEqn

Rearrange equation

b = 0

We found that

y -

intercept

b

is equal to

0 .

Let's substitute that into the equation in slope-intercept form.

y = 625 x + b ⇕ y = 625 x + 0 ⇕ y = 625 x

Now we can use this equation to determine how much money the Rockwell family should budget for

12

months. Let's substitute

x = 12

into the equation.

y = 625 x

Substitute

$x = 12$

y = 625 (12)

Multiply

y = 7500

We found that Rockwell family should budget

7500

dollars for

12

months.

Exercise