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Question: What is the slope and y – intercept of the line \(x+2y=4\)?...

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

Explanation

Solution

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+cy=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=4x+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+cy=mx+c, where ‘m’ represents the slope and ‘c’ represents the intercept on the y – axis. We have the equation x+2y=4x+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,
2y=4x\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,

& \Rightarrow y=2-\dfrac{1}{2}x \\\ & \Rightarrow y=\left( -\dfrac{1}{2} \right)x+2 \\\ \end{aligned}$$ On comparing the above equation with the general form $$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.