need help finding linear slope, what is x in this algebra problem, 6x+7y=42, can anyone help?

Answer 1

x=7+7/6y

Answer 2

The "slope" answers the question: if x becomes one more, what happens to y?

Now suppose that for a certain point (x,y) it is true that 6x + 7y = 42. That means the point lies on the line.

If x becomes one more, then 6x becomes six more. If we would stop here, the left side of the formula would be 48, not 42.

In order to get the 42 again, we must change make 7y six smaller than it was. If 7y decreases by 6, then y decreases by 6/7.

Conclusion: if x increases with 1, y must decrease by 6/7. The slope is therefore -6/7.


(Of course, this can be made into a general rule. If a line is given by the formula a x + b y = c, where a,b,c are number, then the slope is equal to -a / b.)

Answer 3

http://www.1728.com/distaIn mathematics, slope (designated by the letter 'm') is defined as the ratio of the 'Y' axis to the 'X' axis between 2 points. In less formal terms this is called the "rise over the run".
The formula for determining the slope between 2 points is:


Slope = m = (Y2 -Y1) ÷ (X2 -X1)
In the above graph we have 2 points where 'a' has the values of x=1 y=2 and the values of point 'b' are x=5 y=4. The math "shorthand" for this is a(1,2) and b(5,4).
Using the formula, we can determine a linear equation's slope from these 2 points.

m = (4 - 2) ÷ (5 - 1)
m = 2 / 4
m = .5
Now, if we want to calculate the slope angle we merely take the arc tangent of the slope. In this case, arc tangent(.5) = 26.565...degrees.

Utilizing the Pythagorean Theorem, the distance between the two points is:


Distance = Square Root ( (X difference)2 + (Y difference)2 )
Distance = Square Root ( 22 + 42 )
Distance = Square Root ( 20 )
Distance = 4.4721 ...
We can now formulate a linear equation, the standard form of which is:

y = mx + b
We know the slope so now we must calculate b.
The equation can be re-written as:
b = y -mx

Let's take one of the 2 given points (1, 2) and "plug it in" to the formula.
b = 2 -.5*1
and therefore b=1.5
(NOTE: b is also the y-intercept, which is the y-value where the equation intersects the y-axis.)
As a double check, we can use the other point (5,4) and get b= 4 -.5*5 = 4 -2.5 = 1.5
So, the equation shown in the above graph is:


y = .5x + 1.5


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When Slope and 1 Point Are Known
Example: A line has a slope of 9 and passes through the point (7,5). What is the equation?
From the above example, we can use the formula:


b = y - mx
b = 5 - 9•7
b = -58
Putting this in standard form:

y = 9x -58
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Answer 4

yes i can help you

write the equation as y = ax + b, then the slope is a.

thus first step is

6x+7y=42 <=> 7y = 42 - 6x <=> .....

Answer 5

(slope) m=(y1-y2)/x1-x2
6x+7y=42
=> 7y=42-6x
y=6-6x/7
y=6(1-x/7)
y=6/7(7-x)
slope= -6/7

Answer 6

m = slope = rise over run = (y2-y1)/(x2-x1)

or as m in:

y = mx+b

solve the equation for y:
7y = -6x+42
y = -(6/7)x + 6

the slope is therefore -6/7

Answer 7

x = 7 - 7y

Answer 8

d/dx(6x+7y)=d/dx(42)
6+7dy/dx=0
7dy/dx=-6
dy/dx=-6/7
therefore slope is -6/7

Answer 9

x= -7/6y+7