Question

How do you draw the line of the $ x$ intercept of $ 3$ and $ y$ intercept of $ 5$ ?

Answer 1

Hint: The line when given by its Cartesian values which is its $ x$ values is of the form $ ax + by + c = 0$ But when we are given the $ x$ intercept and the $ y$ intercept there is also a very simple formula to calculate the equation of the required line in its Cartesian coordinate, which only used the $ x$ and the $ y$ intercept. The formula is as follows:
 \[\dfrac{x}{a} + \dfrac{y}{b} = 1\] where $ a$ and $ b$ are the $ x$ and $ y$ intercepts respectively. Thus to solve the questions we will put the values of the intercepts given in the question into the following formula and achieve the equation of the desired line.

Complete step-by-step answer:
The $ x$ and the $ y$ intercept of the line are the points where the given line cuts the $ x$ and the $ y$ axes in the Cartesian plane. The equation of line when both the $ x$ and the $ y$ intercepts are given is calculated by using the formula:
 \[\dfrac{x}{a} + \dfrac{y}{b} = 1\] where $ a$ and $ b$ are the $ x$ and $ y$ intercepts respectively. We are given the $ x$ and the $ y$ intercepts as $ 3$ and $ 5$ respectively. Putting the values of $ x$ and the $ y$ intercepts we get,
 \[\dfrac{x}{3} + \dfrac{y}{5} = 1\] which upon solving can be elegantly written as:
 \[5x + 3y - 15 = 0\] which is the desired equation.

Note: The intercept form and the slope intercept form of the line in its Cartesian coordinates must be remembered by heart .
The intercept form is given below
 \[\dfrac{x}{a} + \dfrac{y}{b} = 1\] where $ a$ and $ b$ are the $ x$ and $ y$ intercepts respectively.The slope intercept form also comes in handy at times the slope intercept form is as follows:
 \[y = mx + c\] where $ m$ is the slope and $ c$ is the $ y$ intercept of the line.