whats the equation of the parell line to the point of (3,-3) and 2x+3y=15

Answer 1

The slope-intercept form for a line is y = mx + b.

We must find a line that is parallel to the given line. We know that parallel lines have the same slope.

So we must find the slope of the given line. 2x + 3y = 15.

We solve this equation for y: First subtract 2x from both sides.

3y = -2x + 15 Next divide both sides by 3.

y = -2/3 x + 5 Now we know the slope. It is next to the x. -2/3

So our answer has this value for m.

y = -2/3 x + b. Now we must make this line pass through the point (3, -3)

So we will insert. 3 in for x and -3 in for y and solve for b.

-3 = (-2/3) (3) + b

-3 = -2 + b Add 2 to both sides.

-1 = b

We now have all we need to put the equation together: m = -2/3 and b = -1

So in y = mx + b, we have. y = -2/3 x - 1

This is the answer in slope intercept form. If you want to put it in standard form, clear the fraction by multiplying by 3 and rearrange in Ax + By = C format. (That means x's first, y's second, then equal, then the constant.

Hope this helps.

Answer 2

Hi Dearicka,

Recall that parallel lines have the same slope. Recall also that the slope-intercept form of the equation of any line is y=mx + b where:

y=y-coordinate

x=x-coordinate

m=slope

b=y-intercept

Now, we don't have that form here, but we can convert to it:

2x+3y=15

Subtract 2x from both sides:

3y= -2x + 15

Isolate y; divide both sides by 3:

y= -2/3x + 5

Now, we have our y=mx + b equation and we have our slope:

m= -2/3

Again, parallel lines have the same slope, and you were given coordinates, so for your parallel line equation:

y=-3

x=3

m=-2/3

Let's find b:

-3=(-2/3)(3) + b

-3= -2 + b

b=-1

Equation of parallel line:

y= -2/3x -1

That's slope-intercept form; for general form ax + by = c, we again convert but this time in reverse:

Subtract y on both sides:

-2/3x-y-1=0

-2/3x - y=1

If your instructor requires whole number coefficients, we can multiply everything by 3:

-2x-3y=3

I hope this helps.

Answer 3

First, find the slope of the given line.

2x+3y=15 Subtract 2x from both sides of the equation.

3y=-2x+15 Divide both sides by 3

y=-2/3x+5

The slope of this line is -2/3. So the slope of the line parallel to this line is m=-2/3 Now find the equation of a line with this slope through the given point.

(3,-3) is (x1,y1)

y-y1=m(x-x1) plug in the values

y-(-3)=-2/3(x-3) Distribute the -2/3 and simplify the left side

y+3=-2/3x+2 Subtract 3 from both sides of the equation

y=-2/3x-1