Question

Harry owes $8400 to the bank. He makes the same payment each month. After 10 months, he will owe $6900.Use the points (0, 8400) and (10, 6900) to find the slope. Then use that slope and the y-intercept to write an equation modeling this situation.Write your equation in the form y = mx + b.View keyboard shortcuts12ptParagraph

Answer 1

The answer is: y = - 150x + 8400

The two points are given in the (x, y) format. Meaning that

x1= 0 and y1 = 8400, while

x2 = 10 and y2 = 6900.

We are required to find the slope given two points (0, 8400) and (10, 6900).

This is easily done if we use the slope formula.

The slope formula is given below:

`\begin{gathered} m=(y_2-y_1)/(x_2-x_1) \\ m=\text{Slope} \end{gathered}`

Now we can proceed to finding the slope:

`\begin{gathered} m=(6900-8400)/(10-0)=-(1500)/(10) \\ \\ \therefore m=-150 \end{gathered}`

Now that we have the slope (m), we can also find the intercept (b) using the equation given in the question:

`y=mx+b`

Here we shall use any of the coordinates: (10, 6900) or (0, 8400)

Using (10, 6900) implies: x = 10 and y = 6900

Substituting these values into the equation above:

`\begin{gathered} y=mx+b \\ y=6900, \\ x=10 \\ m=-150 \\ \\ 6900=-150*10+b \\ 6900=-1500+b \\ \text{add 1500 to both sides} \\ \\ 6900+1500=-1500+1500+b \\ 8400=b \\ \therefore b=8400 \end{gathered}`

Since we now have slope (m) and intercept (b), we can therefore write the equation as follows:

`\begin{gathered} y=mx+b \\ m=-150 \\ b=8400 \\ \\ \therefore y=-150x+8400 \end{gathered}`

The final answer is: y = - 150x + 8400