Question

How do you find the X and Y intercepts for $ 3x + 6y = 18? $

Answer 1

Hint: Intercept can be defined as the line which intersects the x-axis or the y-axis. In the standard formula $ y = mx + b $ where b is the intercept of the given equation. There is y-intercept when x is equal to zero and x-intercept when y is equal to zero.

Complete step by step solution:
First of all we will find the “x” intercepts which occur on the “x” axis when $ y = 0 $ , so find the value for x.
Take the given expression: $ 3x + 6y = 18 $
Place $ x = 0 $ in the above equation.
 $ 6y = 18 $
Now, take the coefficient on the opposite side and make the subject “x”. term multiplicative on one side if moved to the opposite side then it goes to the denominator.
 $ \Rightarrow y = \dfrac{{18}}{6} $
Removing common factors from the numerator and the denominator.
 $ \Rightarrow y = 3 $
So, the y-intercept is at the $ (0,3) $ ….. (A)
Now, similarly for the x intercepts when $ y = 0 $
Take the given expression: $ 3x + 6y = 18 $
Place $ y = 0 $ in the above equation.
 $ 3x + 6(0) = 18 $
Simplify the above equation and also apply that when zero is multiplied with any number gives zero as the resultant value.
 $ 3x = 18 $
Term multiplicative on one side if moved to the opposite side then it goes to the denominator.
 $
  x = \dfrac{{18}}{3} \\
  x = 6 \;
  $
So, the x-intercept is at the origin $ (6,0) $ … (B)
Hence, the equations (A) and (B) are the required solution.

Note: Always remember the standard form of the linear equation, slope and intercept equation as the y intercept depends on the standard equation. Also, know the basic identities to simplify the equation such as zero when multiplied with any number always gives the resultant value as zero.
In any linear equation, m is the slope and b is the y-intercept and this equation is known as the slope-intercept equation.