Question

How do you write the standard form of the equation given $\left( {2,4} \right)$and slope $- 1$?

Answer 1

We know that the standard equation of line is $y = mx + c$. First of all, we will put the values of given coordinates and slope in this equation. This way, we can find the value of the y-intercept. After that, we will put the values of slope and y-intercept in the standard equation so to get our final answer.

Complete step by step answer:
We are given coordinates of a point $\left( {2,4} \right)$ and slope $- 1$ from which we need to find the standard form of equation of line.
We know that the line can be expressed as a standard form by the equation $y = mx + c$.
We will put $x = 2$, $y = 4$ and slope $m = - 1$in this equation.
$y = mx + c \\\ \Rightarrow 4 = ( - 1)(2) + c \\\ \Rightarrow 4 = - 2 + c \\\$
Now, we can say that this has become the linear equation with variable $c$and by solving it we can get the value of $c$which is the y-intercept of the given line.
We can rewrite this equation as:
$\Rightarrow 4 = c - 2$
Here, we can see that 2 is subtracted from the variable on the right hand side of the equation. Therefore, to remove it, we can add 2 to both the sides of the equation.
$\Rightarrow 4 + 2 = c - 2 + 2 \\\ \Rightarrow 6 = c \\\ \Rightarrow c = 6 \\\$
Thus, we have the value of the y-intercept which is 6.
Now we will put the value of the slope and y-intercept in the equation $y = mx + c$.
Therefore, we get the standard form of the equation $y = - x + 6$or we can also write it as $x + y = 6$.

Note: Here, we have determined the value of $c$by solving the linear equation. While solving any linear equation, we need to keep in mind that whatever operation we perform, we have to perform it on both the sides of the equation. This is because the equation must be in balanced condition.