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

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

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.

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