Question

What are the intercepts of \[y = 2x - 4\] ?

Answer 1

Hint: In this question, we have to find out the intercepts of a given equation.
The equation of a line which cuts off intercepts a and b respectively from the $ x $ and $ y $ axes is \[\dfrac{x}{a} + \dfrac{y}{b} = 1\] ,
 \[a = {\text{ }}x\] -intercept value of the linear equation.
 \[b = {\text{ }}y\] -intercept value of the linear equation.
To find the intercepts we will compare the given equation with \[\dfrac{x}{a} + \dfrac{y}{b} = 1\] and finding the value of $ a $ and $ b $ we will get the required intercepts.

Complete step by step solution:
We have to find out the intercepts of \[y = 2x - 4\] .
We know that the intercept form of a straight line equation is \[\dfrac{x}{a} + \dfrac{y}{b} = 1\] ……i),
Where
 \[a = {\text{ }}x\] -intercept value of the linear equation.
 \[b = {\text{ }}y\] -intercept value of the linear equation.
Now we can write the given equation as \[2x - y = 4\]
Or, \[\dfrac{{2x}}{4} - \dfrac{y}{4} = 1\]
Or, \[\dfrac{x}{{\dfrac{4}{2}}} + \dfrac{y}{{ - 4}} = 1\]
 \[\dfrac{x}{2} + \dfrac{y}{{ - 4}} = 1\] .……...ii)
Comparing equation i) and ii) we get,
  \[a = {\text{ }}x\] -intercept = \[2\] .
 \[b = {\text{ }}y\] -intercept = \[ - 4\] .
Hence, the intercepts of \[y = 2x - 4\] are \[2\] and \[ - 4\] .

Note: Linear equation:
Any equation which can be put in the form \[ax + by + c = 0\] , where $ a $ , $ b $ and $ c $ are real numbers, $ a $ and $ b $ are not both zero, is called a linear equation in two variables.
Another method:
We have to find out the intercepts of \[y = 2x - 4\] .
This is the equation of a line. When the line crosses the \[x\] -axis, the $ y $ -coordinate at this point will be zero. By substituting \[y = 0\] into the equation will give us the \[x\] -intercept.
i.e. \[0 = 2x - 4\]
 \[2x = 4\]
Therefore, \[x = \dfrac{4}{2} = 2\]
Similarly, when the line crosses the $ y $ -axis, the \[x\] -coordinate at this point will be zero and substituting \[x = 0\] into the equation will give us the y-intercept.
i.e. \[y = 2 \times 0 - 4\]
Hence, \[y = - 4\]
Hence, the intercepts of \[y = 2x - 4\] are \[2\] and \[ - 4\] .