Question

How do you find the intercepts for $x + 2y = 10$ ?

Answer 1

Hint:For finding the intercepts, First put $x = 0$ and then find the value of $y$ . The resulting coordinates are to be noted and then plotted. Now, put $y = 0$ and then find the value of $x$ . Note down the value of the coordinates. When $y = 0$ it is known as $x$ -intercept and when $x = 0$ it is known as the $y$ -intercept.

Complete step by step answer:The given linear equation is: $x + 2y = 10$
For finding the intercepts of the linear equation,
Firstly, we put $x = 0$ and find $y$
$\Rightarrow (0) + 2y = 10$
Now divide with $2$ into both sides of the equation.
$\Rightarrow \dfrac{{2y}}{2} = \dfrac{{10}}{2}$
On simplifying we get,
$\Rightarrow y = 5$
$\Rightarrow$ The $x$ -intercept is $5$
For the $y$ -intercept , we put $y = 0$ and then find the value of $x$
$\Rightarrow x + 2(0) = 10$
$\Rightarrow x + 0 = 10$
Evaluate the whole equation
$\Rightarrow x = 10$
$\Rightarrow$ The $y$ -intercept is $10\;$
$\therefore$ The $x$ -intercept and the $y$ -intercept for the equation $x + 2y = 10$ are given by $5,10\;$ respectively.

Additional information: Whenever the slope of a line $m$ is $\infty$ it indicates that the equation is a straight line parallel to the $y$ axis. If the slope of the line $m$ is $0$ , then it indicates that the equation is a straight line parallel to the $x$ axis. The slope is also known as the “gradient”.
Here in the given equation, $x + 2y = 10$ the slope is given by $m = \dfrac{{ - 1}}{2}$ .

Note:
$x$ -intercept is where the given linear line equation touches the $x$ -axis. $y$ -intercept is where the given linear line equation touches the $y$ -axis. After getting an answer, one must always cross-check by substituting the values back in the equation to see if they are correct. Both the values should be taken for substitution to prove that they lie on the given linear equation.