Question

How do you find the slope of $-2x+4y=6$ ?

Answer 1

For finding the slope of the given equation $-2x+4y=6$ that is the equation of a line, we will convert the equation of line in the form of $y=mx+c$ by addition, subtraction, multiplication or division. Then we will compare the obtained equation with $y=mx+c$ and find the value of $m$ that denotes the slope of the equation.

Complete step by step solution:
Since, the given equation is the equation of line that is:
$\Rightarrow -2x+4y=6$
Now, we will apply addition, subtraction multiplication or division according to the requirement of the process to convert this equation in the form of $y=mx+c$ . So, first of all we will place $y$ one side of the equation and other values other side of the equation as:
$\Rightarrow 4y=6+2x$
When we place any value from one side to the other side of an equal sign we will change the sign related to that value like addition will be subtraction or subtraction will be addition and multiplication will be division and division will be multiplication. So, we changed the sign of $2x$ by this method.
Now, we will write the above equation in a proper sequence as:
$\Rightarrow 4y=2x+6$
Here, we will divide by $4$ both sides of the above equation as:
$\Rightarrow \dfrac{4y}{4}=\dfrac{2x+6}{4}$
In the above equation, $4$ will cancel out the multiplication of $y$ that is also $4$ and we will write the $\dfrac{2x+6}{4}$ as $\dfrac{2x}{4}+\dfrac{6}{4}$ in the above equation:
$\Rightarrow y=\dfrac{2}{4}x+\dfrac{6}{4}$
Since, $2$ is the common factor for numerator and denominator in the above equation. So, we can simplify the above equation as:
$\Rightarrow y=\dfrac{1}{2}x+\dfrac{3}{2}$
Now, we will compare the above equation with the equation $y=mx+c$ and will get the value of $m$ as:
$\Rightarrow m=\dfrac{1}{2}$
Hence, the slope of the equation $-2x+4y=6$ is $\dfrac{1}{2}$ .

Note: Slope of a line is the same at every point of that line no matter which point you are taking. It just shows the direction of the line. We can calculate the slope of line by dividing the difference of any two points of y axis by the difference of any two points of x axis as:
$\Rightarrow m=\dfrac{{{y}_{2}}-{{y}_{1}}}{{{x}_{2}}-{{x}_{1}}}$