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.