Question
Question: How do you find the slope of the line whose equation is \[2x - 4y = 10\]?...
How do you find the slope of the line whose equation is 2x−4y=10?
Solution
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:
⇒2x−4y+4y=10+4y
⇒2x=10+4y
Now, we can subtract 10 from both the sides of the equation, and we get:
⇒2x−10=10+4y−10
⇒2x−10=4y
This can also be written as:
⇒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:
⇒y=42x−10
Now, we will separate the term on the right side of the equation, and we get:
⇒y=42x−410
When we cancel the numerator and denominator, then we get:
⇒y=2x−25
This can also be written as:
⇒y=21x−25
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=21and c=−25
Therefore, we get that the slope of the line 2x−4y=10is 21.
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.