Question

What is the equation of the line that has a y-intercept of (0, -3) and passes through the point (-9, -9)?
Stack and Subtract
y

Answer 1

Answer:

$\sf 3x - 2y - 6 = 0$

Step by step explanation:

Two points are given to us and we need to write the equation of the line that passes through the given two points .

• Firstly let's find the slope of the line which is difference of ordinate divided by difference of x coordinates .

$\sf\implies m=\dfrac{y_2-y_1}{x_2-x_1} \\\\\sf\implies m =\dfrac{-9-0}{-9+3} \\\\\sf\implies m = \dfrac{-9}{-6} \\\\\sf\implies \boxed{\sf m =\dfrac{3}{2}}$

• Now we can use the point slope form of the line .The point slope form of the line is $\sf y-y_1 = m(x-x_1)$ . On substituting the respective values ,

$\implies\sf y - y_1 = m(x - x_1) \\\\\sf \implies y -(-3) = \dfrac{3}{2}(x -0) \\\\\sf\implies 2( y +3 ) = 3x \\\\\sf\implies 2y + 6 = 3x \\\\\sf\implies \boxed{\pink{\frak{3x - 2y - 6 = 0 }}}$