Question

>

Paul and Seth know that one

point on a line is (4,2) and the

slope of the line is -5. Each

student wrote a different

equation relating x and y.

Paul

Seth

Y-Y

A. Do the two equations

represent the same line?

Construct a mathematical

argument to support your

answer.

y = mx + b

2 = 5(4) + b

2 = -20 + b

22 = 6

y = -5x + 22

m =

X2 - x

-5=

y-2.

X-4

5(x - 4) = y-2

Answer 1

They both represent the same equation

Explanation:

Given

`Point\ (x,y) = (4,2)`

`Slope,\ m = -5`

The question is not properly presented.

However, I can pick the following from the question.

Paul's workings:

`y = mx + b`

Where

`y = 2`
`x = 4` and
`m = -5`

So:

`2 = -5*4 + b`

`2 = -20 + b`

`b = 2+20`

`b = 22`

Seth's workings:

`m = (y - y_1)/(x - x_1)`

`m(x - x_1) = y - y_1`

`-5(x - 4) = y - 2`

Required

Determine if both workings represent the same equation

Step 1: Analyze Paul's workings

Paul applied slope intercept to determine the equation of the line and his workings is correct.

Step 2: Analyze Seth's workings

Seth applied slope formula in determining the equation of the line and up till where Seth's stopped, Seth was correct.

The next step is to complete Seth's workings as follows:

Seth's workings:

`m = (y - y_1)/(x - x_1)`

`m(x - x_1) = y - y_1`

`-5(x - 4) = y - 2`

Open bracket

`-5x + 20 = y - 2`

Collect Like Terms

`-5x + 20 + 2 = y`

`-5x + 22 = y`

Reorder

`y = -5x + 22`

Comparing the end results of Seth and Paul's workings.

We have that both results are the same.

i.e.

`y = -5x + 22`

Hence, they both represent the same equation