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.