Question

What is the slope and y – intercept of the line $x+2y=4$?

Answer 1

Hint: Write the given equation in the slope – intercept form by leaving the term containing the variable y to the L.H.S and taking all other terms to the R.H.S, make the coefficient of y equal to 1 by dividing both the sides with 2. Now, compare the given linear equation with the slope – intercept form of a line given as \[y=mx+c\]. Here, ‘m’ is the slope of the line and ‘c’ is its y – intercept. Write the respective values of m and c to get the answer.

Complete step by step solution:
Here we have been provided with the linear equation $x+2y=4$ and we have been asked to find the slope and y – intercept of this line. Let us first know about the slope – intercept form of a linear equation.
Now, we know that we can write a linear equation of a straight line in many forms like: - standard form, slope – intercept form, polar form, parametric form etc. But here let us know about the slope – intercept form.
In slope – intercept form we write the equation of a line as \[y=mx+c\], where ‘m’ represents the slope and ‘c’ represents the intercept on the y – axis. We have the equation $x+2y=4$ so we need to leave the term containing the variable y in the L.H.S and take all the terms to the R.H.S. So we get,
\[\Rightarrow 2y=4-x\]
Now, we need to make the coefficient of y equal to 1, so dividing both the sides with 2 we get,
\[\begin{align}
  & \Rightarrow y=2-\dfrac{1}{2}x \\
 & \Rightarrow y=\left( -\dfrac{1}{2} \right)x+2 \\
\end{align}\]
On comparing the above equation with the general form \[y=mx+c\] we can conclude the following results: -
$\therefore $ Slope (m) = $\left( -\dfrac{1}{2} \right)$ and y – intercept (c) = 2.

Note: Note that you can also convert the given equation of line into the standard form given as \[ax+by+c'=0\]. Here, slope is given as \[\dfrac{-a}{b}\] and the y – intercept for this form is given as \[\dfrac{-c'}{b}\]. In the intercept form we write the equation as $\dfrac{x}{a}+\dfrac{y}{b}=1$ where ‘a’ and ‘b’ are the x – intercept and y – intercept respectively. The negative value of the slope states that the line is forming an obtuse angle with the positive direction of x – axis.