The end of the third month this year, you have $510 saved. At the end of the seventh month this year, you have saved $626.

Question

The end of the third month this year, you have $510 saved. At the end of the seventh month this year, you have saved $626.Write an equation to model this situation (use  for months and  for savings).

Answer 1

Great question. This question mainly is trying to find the equation of a line.

A line has the general form y = mx + b, where m is the slope and b is the y-intercept.

Because we have to use m and s, our equation is s = xm + b where s is savings and m is months.

In our given problem, we have the points (3, 510) and (7, 626) since we know there is $510 saved in the third month and $626 saved in the seventh.

We can first use these two points to find the slope of our line.

Slope = Rise / Run = Change in Y / Change in X

We can thus conclude that the slope = (626 - 510) / (7-3)

116 / 4

Slope = 29

So we have one part of our line. Now we need to find the y intercept. We can use point-slope form for that with one of the points given.

Point slope form has the general form y-y₁ = slope(x-x₁) where y₁ and x₁ are a coordinate of the line.

s - 510 = 29(m-3)

s = 29m-87+510

s = 29m + 423