Question

How do you find the slope of 4x + y = 7?

Answer 1

Hint: We are given an equation of line as 4x + y = 7. We are asked to find the slope of it. We will first learn what a slope is and then we will focus on various methods to find the slope. We will learn what slope is and find using \[\tan \theta \] and also by \[m=\dfrac{rise}{run}.\] We will learn about the slope intercept form and then we will convert our problem to slope intercept form and then we will find the slope.

Complete step by step answer:
We are given an equation as 4x + y = 7. We are asked to find the slope of the given equation. We will first understand what the slope means and then we will focus on the ways to find the slope of any given equation. Now, the slope of any line is the angle made by the line with the positive x-axis. We generally find the slope by finding the ratio of rise and run. Rise means the movement of the function along the y – axis while run refers to the movement along the x – axis. So, one way is \[\text{slope}=\dfrac{rise}{run}.\] Another way is to find the term of the angle made by the line with x-axis. So, \[\text{Slope}=\tan \theta .\]

The slope is denoted as m, so, \[m=\tan \theta \] or \[m=\dfrac{rise}{run}.\] Other ways to find the slope is to use the equation given to us. The general equation of line in standard form is given as ax + by + c = 0. We can convert this equation to slope intercept form given as y = mx + c where m is the slope. So, we can find the slope from here.
Now, we have 4x + y = 7. So, we will transform this into slope intercept form. So, we will use the algebraic tools to change it into the slope intercept and then we will get the slope. We have 4x + y = 7. We will subtract 4x to both the sides, we get,
\[4x+y-4x=7-4x\]
On simplifying, we get,
\[\Rightarrow y=-4x+7\]
Now comparing this with our slope intercept form y = mx + c, we can see that we have, m = – 4. So, the slope of 4x + y = 7 is – 4.

Note:
Another way which is too direct to find the slope is as we know the standard form of the line is given as ax + by + c = 0, then we know slope is given as \[\dfrac{-a}{b}\] where a is the coefficient of x and b is the coefficient of y. Now in our equation, 4x + y = 7, we have a = 4, b = 1. So, using the above trick, the slope will be \[m=\dfrac{-a}{b}.\]
Using the above value, we get,
\[\Rightarrow m=\dfrac{-4}{1}\]
On simplifying, we get,
\[\Rightarrow m=-4\]