Question

How do you find the x and y intercept of $9x + 8y = - 24$?

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 answer:
First of all we will find the “x” intercepts which occur on “x” axis when $y = 0$, so find the value for x.
Take the given expression: $9x + 8y = - 24$
Place $x = 0$in the above equation.
$8y = - 24$
Now, take the co-efficient 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{{24}}{8}$
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: $9x + 8y = - 24$
Place $y = 0$in the above equation.
$9x + 8(0) = - 24$
Simplify the above equation and also apply that when zero is multiplied with any number gives zero as the resultant value.
$9x = - 24$
Term multiplicative on one side if moved to the opposite side then it goes to the denominator.
$
  x = - \dfrac{{24}}{9} \\
  x = - \dfrac{8}{3} \\
 $
So, the x-intercept is at the origin $( - \dfrac{8}{3},0)$ … (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.