Question

The equation of the following line in double intercept form, the x-intercept and the y-intercept are respectively.
x + y = 2
A. \[\dfrac{x}{2} - \dfrac{y}{2} = 1,a = 2,b = - 2\]
B. \[ - \dfrac{x}{2} + \dfrac{y}{2} = 1,a = 2,b = - 2\]
C. \[\dfrac{x}{2} + \dfrac{y}{2} = 1,a = 2,b = 2\]
D. \[\dfrac{x}{2} - \dfrac{y}{2} = 1,a = - 2,b = 2\]

Answer 1

Hint: To find the intercept in both axes made by a line, you need to get 1 on the right side of the equation of the given line equation by multiplying or dividing by some number.

Complete step-by-step answer:
The equation of the given line: \[x + y = 2\]
Now, to find the x and y intercept we need to get 1 on the right side of the equal sign by multiplying or dividing accordingly.
As we have 2 on the right side of the equal sign, we need to divide both sides by 2, in order to get 1 on the right side of the equation.
So dividing, we have,
\[ \Rightarrow \dfrac{x}{2} + \dfrac{y}{2} = 1\] ------(1)
Now the x intercept a= 2 and the y intercept , b =2
Hence the correct option is (C)

Note: The intercept form of line is given by \[\dfrac{{\text{x}}}{{\text{a}}}{\text{ + }}\dfrac{{\text{y}}}{{\text{b}}} = 1\], where a is the x intercept and b is the y intercept.
To convert an equation of line into intercept form just divide it by constant term.