what is an equation equal of a line parallel to y=2/3x-4 and goes through the point (6,7)

Question

i cant figure it out

Answer 1

Hello Heather,

For a line to be parallel it must have the same slope as another line therefore:

y = mx +b translated from your data would be

(1) y = 2/3x + b

now we know if x =  6 then y = 7, so solve for the intercept this way

7 = 2/3(6) + b

Then substitute b in the original equation (1)

Once you have the equation of the new line then confirm that (6,7) is a point by substitution as I have done this already. You can plot both lines to be sure but they will be parallel.

The interesting notion about this question is that it almost makes you think that both lines have the point (6,7) common but that is not the case.

Hope this helps!!

Art

Answer 2

Parallel lines have the same slope, so the slope of the equation you are looking for would be 2/3.

The only information missing now is the y-intercept. The slope of the line you are looking for is 2/3: slope represents rise/run or another way to say it is for every 3 points the line moves to the right, it must move 2 points upward. You also know that the line passes through point (6,7), remember points are represented as (x,y), so for this particular point x=6 and y=7. You are looking for the Y-intercept, the Y-intercept is the point where the line crosses the y-axis which by definition is where x=0, so you want to move your (6,7) point to (0,y) in order to get the y-intercept. The key to solving the problem is to notice that the slope moves by 3 points at a time on the x-axis and at the same time the point on the line given to you in the question is 6 points on the x-axis; 3 divides into 6 evenly! If you reduce the point given to you in the question by 2 groups of 3, then it will be at zero, which is the y-intercept. Since you reduced the x-axis by two groups, you need to reduce the y-axis by two groups, and since each group of the y-axis moves by two, you reduce the y point by four. the y point started out as 7, so now it is 3.

your answer is y=2/3x+3

Answer 3

y=2/3x -4

has parallel lines with the same slope =2/3

= the coefficient of the x term when the linear equation is solved for y

y=2/3x +b where b= any number except -4. if b=-4, it's not a parallel line. it's the same identical line

to go through the point (6,7) preplace x ith 6 and y with 7. then solve for b.

7= 2(6)/3 + b

b = 7-4=3

the parallel line is y=2/3x +3

That's the likely answer you want.

if you meant y= (2/3)x-4 as the given line

But there's an ambiguity to the problem

as written it really says y = 2/(3x) -4

or possibly it even meant y= 2/(3x-4)

both these alternatives are rectangular hyperbolas,

with curved hyperbolic lines as the parallel lines

y= 2/(3x) -4 has slope = the derivative = y'

y = 2/(3x)-4 = (2/3)x^-1 -4

y' = -2/(3x^2)

a hyperbolic line with that slope would be the parallel line

it would be helpful to graph the hyperola, to see the lines better

the parallel line is y=2/(3x) +98/9 in order to go through (6,7).

just the same basic rectangular hyperbola

shifted vertically up by 10 8/9=98/9

that's technically the correct answer to the problem as written

Answer 4

Dear Heather,

First, for any line to be parallel to this line, the slope MUST be the same. In this case it is 2/3. Remember slope is calculated using the difference in y values over the difference in x values. That formula is: y2 - y1/x2-x1.

Now, we have the point (6,7) on the line we are looking for. We use the given equation to solve for b, knowing that the equation of a line is y=mx + b.

We can then solve for b now by substituting in the values for x and y given to us. This is what it looks like:

7 = 2/3(6) + b

7 = 4 + b

b then = 3.

We now have our parallel equation as: y = 2/3x + 3

And there we have it!! Good luck on your other problems.

Answer 5

We can also use the point-slope form of a line:

y - y1 = m ( x - x1) since the slope is 2/3 (parallel to the other line with the slope of 2/3) and the line passes through (6,7), so:

Y - 7 = 2/3 (X - 6) Simplifying:

Y = 2/3 X + 3

Answer 6

y= 2/3 x - 4., Parallel lines have equal slop.

y=2/3 x +c ,. C is y intercept. First line's y intercept is -4 , second line is passing through (6 ,7). Second line is 7 units above -4 on y- axis . So -4+7 =3 second line y intercept is 3 .

y = 2/3 x +3.

Proof by substitution,

7=2/3 •6 + C,

7=4+c ,

7-4=c.

c=3.

y=2/3 x + 3.

Answer 7

Parallel lines have same slope.

now, slope m=2/3 with point (6,7).

using the eqn. y-y1=m(x-x1)

→ y-7=2/3(x-6)

→3(y-7)=2(x-6)

→3y-21=2x-12

Therefore, 3y-2x-9=0 is the equation.