Question

Find the intercepts of the equation$2x+5y=10$.

Short answer

The intercepts to the given equation are (5,0) and (0,2).

Step-by-step solution

Given information

The equation is given as$2x+5y=10$to find the intercepts.

Find the intercepts on the abscissa

Apply the definition of the intercepts to find the required answer to the given problem.

• Substitute each $y$by 0 into the given equation and solve to find the intercepts on the abscissa.

$\begin{array}{rcl}2x+5y& =& 10\\ 2x+5\left(0\right)& =& 10\\ 2x& =& 10\\ x& =& \frac{10}{2}\\ x& =& 5\end{array}$

Find the intercepts on the ordinate

Now substitute each $x$by 0 into the given equation and solve to find the intercepts on the ordinate.

$\begin{array}{rcl}2x+5y& =& 10\\ 2\left(0\right)+5y& =& 10\\ 5y& =& 10\\ y& =& \frac{10}{5}\\ y& =& 2\end{array}$