Question

A line that passes through the points (–4, 10) and (–1, 5) can be represented by the equation y = (x – 2). Which equations also represent this line? Check all that apply. 1. y = -5/3 x – 2

2. y = -5/3 x + 10/3

3. 3y = –5x + 10

4. 3x + 15y = 30

5. 5x + 3y = 10

Answer 1

number 2 and 3 is correct.
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Answer 2

The equation y=x-2 do not represents the line that passes through the two point, since for example -4-2=-6, not 10. So (-4,10) is not on the line.
Let find the equation of the line:
First compute the slope using formula:

`(y_2-y_1)/(x_2-x_1)= (5-10)/(-1-(-4))= (-5)/(3)`
So the equation is in the form:

`y=(-5)/(3)x+s\text{ wherein s is another parameter. }`
For x=-4 we get the equation:

`10=(-5)/(3)(-4)+s`
Solving the above equation for s we get:

`s= (10)/(3)`
The equation then is the following:

`y=(-5)/(3)x+(10)/(3)`

The correct answer then is equation 2 and equation 3.