How would I write an equation for a line with the point (7,-6) and parallel to 6x-5y=3? In general form?

Question

I am having trouble writing equations like this with such given information.

Answer 1

Straight lines have (1)slope-intercept form (2)point-slope form equations. In (1) the form is y=mx+b where m is the slope and b is the y-intercept (value of y when x=0). In (2) the form is Y-Ya = m (X-Xa) where m is the slope and (Xa, Ya) a point.

First, you have to understand that since these two lines are parallel, it means that they have equal slopes. Using (1) the slope-intercept form, you can get the slope of 6x-5y=3,
(-5y = -6x + 3 ) / ( -5)
y = 6/5 x - 3/5

slope = 6/5.

Then, since you now have the slope (6/5) and a point (7, -6), you can then use (2) point-slope form to get the equation of the line,

Y-(-6) = 6/5 (X-7)
Y + 6 = 6/5 (X-7)
5Y + 30 = 6X - 42 or in general form Ax + By + C = 0,

6X - 5Y - 72 = 0.

The answer is 6X - 5Y - 72 = 0.
.

Answer 2

*Rewrite the equation in slope-intercept form which is,
y = mx + b

First: subtract 6x from both sides...

6x - 6x - 5y = - 6x + 3
- 5y = - 6x + 3

*Solve for "y" by isolating it > divide everything by - 5 ...

- 5y/-5 = (- 6/-5)x + 3/-5
y = (6/5)x - 3/5

*The slope is a number/fraction beside the "x" which is, 6/5 in this equation. Parallel lines have the same slope, in this case your trying to find an equation for a line with 6/5 as its slope.

Sec: place the point (7, -6) and the slope (6/5) represented as "m" into the point-slope formula: y - first y = m(x - first x)

y - (-6) = 6/5(x - 7)
y + 6 = (6/5)x - 42/5

*The general form is when the equation is set to equal "0" ...

*Add 42/5 to both sides...

y + 6 + 42/5 = (6/5)x - 42/5 + 42/5
y + 72/5 = (6/5)x

*Subtract (6/5)x from both sides...

y + 72/5 + (6/5)x = (6/5)x - (6/5)x
(6/5)x + y + 72/5 = 0

P.S. Steven, your answer is correct but, the general form is set to "0" > all other variable are placed to the left :-)

Answer 3

Algebra was a long time ago. Here is what I remember today: Parallel lines have the same slope.
y=ax+b is the general form where a=slope and b=y-intercept (the value of y where x=zero).
Arrange 6x-5y=3 in general form:
Add 5y to both sides: 5y + 3 = 6x
Subtract 3: 5y = 6x - 3
David by 5: y = 6/5x - 3/5
The line you need is y = 6/5x + b, where (7,-6) is a point on the line. Solve for b:
Subtract 6/5x from each side: b = y - 6/5x
Substitute known point:
b = -6 - 6/5(7) = -6 - 42/5 = (-30 - 42)/5 = -72/5
General form: y = 6/5x -72/5

Some one let me know if I made any major errors.

Answer 4

A general equation for a line parallel to 6x-5y=3 is:
6x-5y=k, where k is a constant ,as their slopes are equal & = 6/5. To find k, we use the given fact that the line passes through the point (7,-6). So:
k=72. The answer is :6x-5y=72.
Check that this Eq.satisfies the two conditions of the problem: Slope of both are equal & = 6/5, so they are paralel.The point (7,-6) satisfies the Eq.so the line passes through this point.

Answer 5

even as some thing says that lines are parallel, what it skill is they have an same slope. to locate the slope of this line, we favor to locate the slope of the line that's parallel to: 2x-3y=11 to help make it a lot less complicated to locate the slope of the line, it helps to notwithstanding the equation in y= mx + b widely used style the position m represents slope, b represents the y-intercept (the position on the graph the line is even as x = 0), and x and y signify places on the graph Parallel line: 2x-3y=11 subtract 2x from both aspect 2x -2x -3y = 11 -2x to get y on my own on the aspect simplify -3y = 11 -2x then divide by using -3 to get y on my own -3y/-3 = (11 -2x)/-3 simplify y = 2/3x -11/3 we are able to tell that the slope of the line is two/3, the x coefficient and m in widely used style. Now that the slope is large-spread, the y-intercept (b) is mandatory to end the equation y=2/3x + b is what all of us recognize so a ways... to be sure out b this equation would nicely be used substituting the coordinate factor (6,-5) for x and y respectively -5 = 2/3(6) + b simplify -5 = 12/3 + b ... -5 = 4 + b ... -5 -4 = 4 -4 + b subtracting 4 from both aspect to get b on my own ... -9 = b Now that the slope (m) and y-intercept (b) are huge-spread, you've all you want and would write the equation for the line : y = mx + b y = 2/3x -9

Answer 6

Line throug point (7,-6)
And paralell to 6x-5y=3.

First right the equation of parrallel line in form of y=mx+c (let y = 1)
I.E
6x-5y=3 Let's take 5y to the other side of =(equal) sign (i.e it will turn to positive)

So our new equation will be 6x=5y+3.

Secondly, we take 3 to the x's side. (3 will turn from positive to negative)

New equation becomes, 6x-3=5y which is same as 5y=6x-3

Thirdle, we make y to be equal to one by dividing both sides of the equation with 5

i.e 5/5y=6/5x-3/5



So our new equation becomes: y=6/5 X - 3/5

NOTE: the gradient of two parallel line are equal.

So The granient is the 6/5 (ie y=mx+c where m is the gradient)

We know that we get gradient of a line from the formula

Change in y/Change in x (change in y divide by change in X)

So

Lets say (y - -6)/(x - 7) = the gradient whic in our case = 6/5

Then cross multiply

5(y - -6)=6(x -7)

then open the brackets. 5y - 30 = 6x - 48

Then collect like terms.
5y=6x-48+30 which is equal to 5y=6x-18

Then make your y=1 by dividing both sides by 5

5/5y=6/5x - 18/8

Hence the answer to your question is

y=6/5 X - 18/8.

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Answer 7

first u want to get the -y by itself so subtract 6x to the right and then the equation will look like this: -5y=3-6y now you have to get rid of the -5 so u divide everything by -5 and your equation should like this y= 3/-5 - 6/-5x. then u plug in the points (7,-6)

Answer 8

A line a'x + b' x = c' is parallel to ax + by = c iff ab' = a'b

So, if you consider any line whose equation is 6x-5y = k, or a multiple of it, you will have a parallel.

Just plug the point coordinates and calculate k.

Ana