Question

(-6,-3) and (-9,-2)

Write the equation of the line passing through the given points. Write the equation in standing form
Ax+By=C

The equation to the line is:

Answer 1

x + 3y = -15

Explanation:

There are 2 ways to find this equation:

The first way: We have: y = ax + b (this is the line, right?)

The line is through the point (-6, -3) so we have:

-3 = (-6)a + b (1)

The line is also through the point (-9, -2) so we have:

-2 = (-9)a + b. (2)

From (1) and (2) we get a equals -1/3, b equals -5. Then:

`y=-(1)/(3) x - 5`

<=>
`x + 3y=-15`

The second way:

Let A(-6, -3) and B(-9, -2), then AB = (-3, 1).

=> The normal vector of this line is n = (1, 3).

The line that is through the points A(-6, -3) and B(-9, -2), and has the normal vector n=(1, 3) has the equation:

`1(x+6) +3(y+3)=0\\x+3y +15=0\\x+3y=-15`