Question

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

Answer 1

This type of problem is based on the concept of equation of line. First, we have to consider the given x-intercept and y-intercept. Using this value, we can form the line-intercept equation, that is, $\dfrac{x}{a}+\dfrac{y}{b}=1$. Here, a=3 and b=2. Then, multiply the whole obtained equation of line by 6. We get an equation of the form Ax+By=C, where A is the coefficient of x and B is the coefficient of y. Here, C is the constant. Thus, we have obtained the standard form of the line.

Complete step by step answer:
According to the question, we are asked to find the standard line equation.
We have been given the x-intercept is 3 and the y-intercept is 2.
We know that the point intercept form of a line is $\dfrac{x}{a}+\dfrac{y}{b}=1$. -----(1)
Here, a is the x-intercept and b is the y-intercept.
According to the question, we find that a=3 and b=2.
By substituting value of a and b in the equation (1), we get
$\dfrac{x}{3}+\dfrac{y}{2}=1$. --------(2)
Let us now take LCM in the equation (2).
We get, $\dfrac{2x+3y}{6}=1$.
Now, we have to multiply the whole equation by 6.
Therefore, $\left( \dfrac{2x+3y}{6} \right)\times 6=1\times 6$.
On cancelling out the common term 6 from the left-hand side of the equation, we get
$2x+3y=1\times 6$.
Simplifying the equation further, we get
$2x+3y=6$ -----------(3)
We know that the standard form of a line equation is Ax+By=C, where A is the coefficient of x, B is the coefficient of y and C is a constant.
Comparing this with equation (3), we find that $2x+3y=6$ is the standard form of a line.
Therefore, the standard form of a line given x-intercept=3, y-intercept=2 is $2x+3y=6$.

Note: We should not get confused with the slope-intercept form and point-intercept form. Here, we should not substitute the value of x-intercept in b and y-intercept in a, which will lead to a wrong answer. Also avoid calculation mistakes based on sign conventions.