Question

How do you write an equation in standard form given point $( - 2,4)$ and slope $- \dfrac{3}{2}$ ?

Answer 1

Hint : We have to show the equation in the form $ax + by = c$ . We can show this by using the point-slope form. That the equation of a line passing through the point $\left( {{x_1},{y_1}} \right)$ and with slope ‘m’ is $\left( {y - {y_1}} \right) = m\left( {x - {x_1}} \right)$ . We use this equation to solve the given problem.

Complete step by step solution:
Given, the point $\left( {{x_1},{y_1}} \right) = ( - 2,4)$ and slope $m = - \dfrac{3}{2}$ .
We have the point slope form $\left( {y - {y_1}} \right) = m\left( {x - {x_1}} \right)$ .
Substituting the values we have,
$\left( {y - 4} \right) = - \dfrac{3}{2}\left( {x - \left( { - 2} \right)} \right)$
$\left( {y - 4} \right) = - \dfrac{3}{2}\left( {x + 2} \right)$
Multiplying ‘2’ on both sides of the equation we have,
$2\left( {y - 4} \right) = - 3\left( {x + 2} \right)$
Expanding the brackets we have,
$2y - 8 = - 3x - 6$
Now separating the terms containing variables to the one side of the equation and constants to the other side of the equation,
$3x + 2y = 8 - 6$
$\Rightarrow 3x + 2y = 2$ . This is the required answer.
So, the correct answer is “3x + 2y = 2”.

Note : In solving equations we need to know the multiplication sign changes. That is we know that the product of two negative numbers will be a positive number. The product of a negative (positive) number and a positive (negative) number results in a negative number.