Question
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=4?
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+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,
⇒2y=4−x
Now, we need to make the coefficient of y equal to 1, so dividing both the sides with 2 we get,