Question

How do you write the equation of a line given $m = - 5\left( {2,4} \right)$ ?

Answer 1

Hint : In order to write the equation we need to find what values are given and we are given with the slope $m = - 5$ and a point $\left( {2,4} \right)$ though which the line will pass. We can use the point slope formula to write the equation for this line which is $\left( {y - {y_1}} \right) = m\left( {x - {x_1}} \right)$ where, slope is $m$ and a point $\left( {{x_1},{y_1}} \right)$ .Just put the values in the Equation given and the result is obtained.

Complete step by step solution:
We are given with the values $m = - 5\left( {2,4} \right)$ where $m = - 5$ and a point $\left( {2,4} \right)$ through which the line will pass.
To get the Equation of the line we would use point slope formula that is $\left( {y - {y_1}} \right) = m\left( {x - {x_1}} \right)$ where, slope is $m$ and a point $\left( {{x_1},{y_1}} \right)$ .
Since, we are given with slope and point so by comparing these two we get:
$m = - 5$ and the point is $\left( {{x_1},{y_1}} \right) = \left( {2,4} \right)$ .
Just the put the values in the above mentioned slope formula and we get:
$\left( {y - {y_1}} \right) = m\left( {x - {x_1}} \right) \\\ \left( {y - 4} \right) = - 5\left( {x - 2} \right) \;$
Solve it further to get the Equation of a line and we get:
$\left( {y - 4} \right) = - 5\left( {x - 2} \right) \\\ y - 4 = - 5x + 10 \\\ y + 5x = 10 + 4 \\\ y + 5x = 14 \\\ y + 5x - 14 = 0 \;$
Writing the Equation in the standard formula of an Equation:
$5x + y - 14 = 0$
Therefore, the equation of a line given $m = - 5\left( {2,4} \right)$ is $5x + y - 14 = 0$ .
So, the correct answer is “ $5x + y - 14 = 0$ ”.

Note : Look for the best methods that can be easily solved to get an equation.
Do not write the values in $\left( {x,y} \right)$ instead of $\left( {{x_1},{y_1}} \right)$ .
In slope intercept form if $c$ is not given then put the values in $\left( {x,y} \right)$ instead of $\left( {{x_1},{y_1}} \right)$ , then calculate $c$ , then write it in the given form.