Question

What is the slope of the line $4x + y = 3?$

Answer 1

As we can see that the given equation is of a straight line and the equation of any straight line is known as the linear equation. The standard form of the equation is $y = mx + b$ where $m$ is the slope of the line and $b$ is the y- intercept. So we can compare the given equation with the standard form and then get the value of the slope.

Complete step by step solution:
Here we have the equation $4x + y = 3$.
First we will check whether the given equation is in standard form or not and if not then we will arrange the terms so that we get the standard form and then we compare.
So we can write the above equation in standard form by isolating $y$, i.e. $y = - 4x + 3$.
Now we can compare the equation with standard form which is $y = mx + b$ where $m$ is the slope of the line. So here we have $m = - 4$.
Hence the slope of the line $4x + y = 3$ is $- 4$.
The graph of the line $4x+y=3$ is as shown below:

Note:
We should know that there is an alternate way of finding the slope of the line too. We know that the standard form of the line is given as $ax + by + c = 0$. So we can find the slope of the equation with the formula $\dfrac{{ - a}}{b}$, where $a$ is the coefficient of $x$ and $b$ is the coefficient of $y$.