Question

How do you write the standard form of a line given x intercept $= 3$ , y intercept $= 2$ ?

Answer 1

We are given a line whose x intercept and y-intercept is given. Here the x-intercept means $y = 0$ and y-intercept means $x = 0$ .
X intercept means $\left( {x,0} \right)$ and y-intercept means $\left( {0,y} \right)$ . As we got two coordinates then we can find the slope of the line using the formula.
$m = \dfrac{{{y_2} - {y_1}}}{{{x_2} - {x_1}}}$
Here $m$is the slope, ${y_2}\& {\text{ }}{y_1}$are the$\;y$ coordinates.${x_1}and{\text{ }}{x_2}$are the $x$coordinates.
Then using the slope intercept form of the equation of a line i.e.$y = mx + b$.
Here $m$is the slope, $b$is the y-intercept. Then using the values we can substitute in the equation and form the standard equation of the line.

Complete step by step answer:
We are given$x$intercept $= 3$ and $y$intercept $= 2$ of a line. We have to find its standard form of the equation.
Here x-intercept means $\left( {x,0} \right)$ i.e. $\left( {3,0} \right)$ and y-intercept means $\left( {0,y} \right)$ i.e. $\left( {0,2} \right)$ . Hence we get two coordinates now using the formula of slope first we will find the slope of the line.

Using the formula of slope $m = \dfrac{{{y_2} - {y_1}}}{{{x_2} - {x_1}}}$
Here ${y_1} = 0,{y_2} = 2,{x_1} = 3,{x_2} = 0$ on substituting these values in the formula we will get:
$\Rightarrow m = \dfrac{{\Delta y}}{{\Delta x}} = \dfrac{{2 - 0}}{{0 - 3}}$
On further solving we will get:
$\Rightarrow m = \dfrac{{ - 2}}{3}$
Then we will use the slope intercept form of the equation of a line is:
$y = mx + c$
Here $m = \dfrac{{ - 2}}{3};c = 2$
Therefore on substituting the value in the equation. Therefore the equation of this line can be written as:
$\Rightarrow y = \dfrac{{ - 2}}{3}x + 2$
Multiplying both the sides by $3$to clear the fraction the equation can be re-written as:
$\Rightarrow 3y = 2x + 6$
Hence the standard equation is $3y = 2x + 6$

Note: In such type questions mainly get confused by reading the word intercepts. Here given x- intercept and y- intercept should be converted into the coordinate form. By using that coordinate form we can easily solve the whole question. If only one intercept i.e. x-intercept is given then by substituting $x$ equals to zero in the equation we can find the value of$y$intercept or vice versa and then from the equation.