Question

How do you find the slope of the line whose equation is \[2x - 4y = 10\]?

Answer 1

Hint: First, we will figure out what type of formula should be used. Here, we know that we need to use the slope-intercept formula. Every equation that is in this form has a slope ‘m’. So, we need to convert the given equation in the question, in the slope-intercept form. This way we can find the slope.

Complete step-by-step solution:
To find the slope, first we have to convert the equation in a slope-intercept form. The slope-intercept form is:
\[y = mx + c\]
Now, our given equation is:
\[2x - 4y = 10\]
We have to convert it into the slope-intercept form. For that, we will add 4y to both the sides of the equation, and we get:
\[ \Rightarrow 2x - 4y + 4y = 10 + 4y\]
\[ \Rightarrow 2x = 10 + 4y\]
Now, we can subtract 10 from both the sides of the equation, and we get:
\[ \Rightarrow 2x - 10 = 10 + 4y - 10\]
\[ \Rightarrow 2x - 10 = 4y\]
This can also be written as:
\[ \Rightarrow 4y = 2x - 10\]
Now, we will try to simplify it. We will try to make ‘y’ alone here. We will shift 4 to the other side of the equation, and we get:
\[ \Rightarrow y = \dfrac{{2x - 10}}{4}\]
 Now, we will separate the term on the right side of the equation, and we get:
\[ \Rightarrow y = \dfrac{{2x}}{4} - \dfrac{{10}}{4}\]
When we cancel the numerator and denominator, then we get:
\[ \Rightarrow y = \dfrac{x}{2} - \dfrac{5}{2}\]
This can also be written as:
\[ \Rightarrow y = \dfrac{1}{2}x - \dfrac{5}{2}\]
Therefore, we got our equation in the slope-intercept form.
Here, from this slope-intercept form we get that the coefficient of ‘x’ is ‘m’ and m= slope. Here, c= y-intercept.
According to the slope-intercept formula, we get that:
\[m = \dfrac{1}{2}\]and \[c = - \dfrac{5}{2}\]

Therefore, we get that the slope of the line \[2x - 4y = 10\]is \[\dfrac{1}{2}\].

Note: Slope is actually the steepness of a line. If a line is aligned or positioned from the bottom left to upper right, then the slope is a positive slope. If a line is aligned from upper left to bottom right, then the slope is a negative slope.