Question

What is the equation of a line through the points (0, 9) and (3, 0)?

Answer 1

Slope of a Line Passing through two points (x₁ , y₁) and (x₂ , y₂) is given by :

$\spadesuit$  $Slope(m) = \frac{y_1 - y_2}{x_1 - x_2}$

Given Points are (0 , 9) and (3 , 0)

here x₁ = 0 and x₂ = 3 and y₁ = 9 and y₂ = 0

⇒ $Slope(m) = \frac{9 - 0}{0 - 3} = -3$

We know that the form of line passing through point (x₀ , y₀) and having slope m is :

y - y₀ = m(x - x₀)

Here the line passes through the point (0 , 9) and (3 , 0)

We can take any one point of the both

let us take (3 , 0)

x₀ = 3 and y₀ = 0 and we found m = -3

Equation of the line :

y = -3(x - 3)

y = -3x + 9

So the Answer is :

Because $m = \frac{9 - 0}{0 - 3}$ ; y = -3x + 9

Answer 2

The first one would be the right answer. Plug in the x and y in the equations to check