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

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:
 $\frac{y_2-y_1}{x_2-x_1}= \frac{5-10}{-1-(-4)}= \frac{-5}{3}$
So the equation is in the form:
$y=\frac{-5}{3}x+s\text{ wherein s is another parameter. }$
For x=-4 we get the equation:
$10=\frac{-5}{3}(-4)+s$
Solving the above equation for s we get:
$s= \frac{10}{3}$
The equation then is the following:
$y=\frac{-5}{3}x+\frac{10}{3}$

The correct answer then is equation 2 and equation 3. 

Answer 2

Number 2 and 3 is correct.
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