Question

You started your dream business. Month 1, you make $1,200 and in 5 months you will have $5,800. Write and solve a linear equation to find out how much money you will make in 9 months.

Answer 1

Explanation:

Lets write a linear equation from two known points

Point 1 = (x1, y1) = (1,1200)

Point 2= (x2,y2)= (5,5800)

The general expression for a linear equation is:

Y-y1 = m (X-x1)

Where:

`m=(y2-y1)/(x2-x1)`

`m=(5800-1200)/(5-1)`

`m=(4600)/(4)`

m= 1150

Therefore, if terms are replaced in the general expression, the linear equation is given by:

Y-1200 = 1150 (X-1)

Y=1150X-1150+1200

Y=1150X+50

Where:

Y= The amount of money you make for the given month

X= Month No.

Answer 2

below

Explanation:

Let's call the number of months since you started the business "x" and the amount of money you make "y". We know two points on this line: (1, $1,200) and (5, $5,800).

From this information, we can write the equation of the line in slope-intercept form: y = mx + b, where m is the slope and b is the y-intercept.

Using the first point, we can solve for b:

$1,200 = m * 1 + b

$1,200 = m + b

b = $1,200 - m

Using the second point, we can solve for m:

$5,800 = m * 5 + $1,200 - m

$5,800 = 6m + $1,200

$4,600 = 5m

m = $920

So the equation of the line is: y = $920x + $1,200

Finally, to find out how much money you will make in 9 months, we can plug in x = 9:

y = $920 * 9 + $1,200

y = $8,280

Therefore, in 9 months, you will make $8,280.