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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 2x4y=102x - 4y = 10?

Explanation

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+cy = mx + c
Now, our given equation is:
2x4y=102x - 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:
2x4y+4y=10+4y\Rightarrow 2x - 4y + 4y = 10 + 4y
2x=10+4y\Rightarrow 2x = 10 + 4y
Now, we can subtract 10 from both the sides of the equation, and we get:
2x10=10+4y10\Rightarrow 2x - 10 = 10 + 4y - 10
2x10=4y\Rightarrow 2x - 10 = 4y
This can also be written as:
4y=2x10\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:
y=2x104\Rightarrow y = \dfrac{{2x - 10}}{4}
Now, we will separate the term on the right side of the equation, and we get:
y=2x4104\Rightarrow y = \dfrac{{2x}}{4} - \dfrac{{10}}{4}
When we cancel the numerator and denominator, then we get:
y=x252\Rightarrow y = \dfrac{x}{2} - \dfrac{5}{2}
This can also be written as:
y=12x52\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=12m = \dfrac{1}{2}and c=52c = - \dfrac{5}{2}

Therefore, we get that the slope of the line 2x4y=102x - 4y = 10is 12\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.