Write an equation that is parallel to the line 2x - 3y = 9 and passes through the point (4, -1).

Answer 1

First, we will write the equation of the parallel line in slope intercept form y=mx+b so that we can clearly see the slope and y intercept:

2x-3y = 9 subtract 2x from both sides

-2x -2x

-3y = -2x + 9 divide both sides by -3

y = -2x/-3 + 9/-3

-2/-3 simplifies to 2/3 because the negative signs cancel out, and 9/-3 simplifies to -3. The equation of the parallel line in the form y=mx+b is

y= 2/3 x -3

The only piece of information that we need from this equation is the slope, which is 2/3.

**PARALLEL LINES HAVE THE SAME SLOPE**

To find the equation for our line, we get to use a slope of 2/3 because parallel lines have the same slope. We have the “m” of our equation and only need to find the y intercept “b”. We can plug in the slope as m= 2/3 and our given ordered pair (4,-1), where x=4 and y=-1, to find b.

y = m x + b

-1 = 2/3*4 + b. Multiply 4 * 2/3 (the 4 only multiplies with the top number)

-1 = 8/3 + b. Subtract 8/3 from both sides to get b alone

-1 -8/3 = b. The common denominator between -1/1 and 8/3 is 3. To reach 3, -1/1 needs to multiply by 3 on top and bottom to become -3/3, and 8/3 can stay the same (it’s already at 3)

-3/3 - 8/3 = b (only the top combines and the bottom stays the same)

-11/3=b

Now that we have m = 2/3 and b = -11/3, we can put the final equation together:

y = 2/3 x - 11/3

Answer 2

So this question has two parts to it. First, we have to find the slope based on the fact that our line is parallel to the line 2x - 3y = 9. Afterwards, we have to find the appropriate y-intercept so that this point passes through (4, -1)

To find the slope of our line, let's convert 2x - 3y = 9 into slope-intercept form (y=mx + b). By adding 3y to both sides and subtract 9 from both sides, we get 2x - 9 = 3y. Dividing by 3, we get 2/3x - 3 = y. This means that the slope of our line, which is parallel to 2x - 3y = 9, must be 2/3.

After that, we can use point slope form (y-y1 = m( x - x1)). Plugging in our slope and the point (4, -1), we get:

y - -1 = 2/3 (x - 4). We can cancel out the double negative and get y + 1 = 2/3 (x-4)

If point-slope form is fine, you have your answer! Alternatively, you can convert this to slope-intercept form by subtracting one from both sides to get: y = 2/3 (x-4) -1. Then, expand the product to get:

y = 2/3x - 8/3 -1

This gets you: y = 2/3x -11/3