Question

How to turn an equation into standard form if it passes through $ (5, - 1) $ , $ m = 2 $ ?

Answer 1

Hint: In the given question, we have been asked to form an equation which passes through $ (5, - 1) $ and has slope $ = 2 $ . In order to proceed with the following question we need to know the point- slope form and standard form of equation. The equation of a line which has a point and a slope is called Point-slope form. Its format is $ y - {y_1} = m(x - {x_1}) $ , where $ ({x_{1,}}{y_1}) $ represent the point through which the line passes and $ m $ represents the slope of the line. To convert it into standard form we’ll have to write it in $ Ax + By = C $ format. Where $ A $ is the constant of variable $ x $ and $ B $ is the constant of variable $ y $ and $ C $ is the constant value.

Complete step by step solution:
We are given,
 $
  {x_1} = 5 \\
  {y_1} = - 1 \\
  m = 2 \\
  $
By putting the values in the equation. We’ll get
 $ \Rightarrow y - ( - 1) = 2[x - 5] $
 $ \Rightarrow y + 1 = 2(x -5) $
After opening the brackets,
 $ \Rightarrow y + 1 = 2x - 10 $
Now, we’ll bring numerical terms on one side
 $ \Rightarrow y = 2x - 11 $
Now, convert it into standard form,
 $ \Rightarrow 2x - y = 11 $
This is the required answer
So, the correct answer is “2x - y = 11”.

Note: While writing the equation in standard form, you need to keep in mind that in standard form coefficients of $ x $ and \[y\] and constant term cannot have any common factor. Also keep the coefficient of $ x $ i.e. $ A $ greater than zero. There are some more forms apart from Slope-point form to write equations of line such as Two-point form, Slope intercept form, Point slope form, Vertical, and Horizontal. Also, we can find the slope of the equation, by dividing the value of $ y $ by value of $ x $ or by calculating $ \tan \theta $ by dividing Perpendicular by Base.