what is the equation of a line that is perpendicular to 6x+3y=2 and that passes through the point -2,4

Question

I have homework  online and it doesn't show me how to do it helped plzz  got to get done today or I fell and have to take the class again help me pleased  hello hello 

 

Answer 1

To find a perpendicular line you have to find the negative reciprocal of the original slope. The equation is not in y=mx+b form so it is easiest if you convert it to:

 

y=2/3-2x. From this you can see that the negative reciprocal is 1/2. Now you have two points given to you that you can plug in to find the b in your mx+b equation. The -2 goes in for the x and the 4 goes in for the y. This gives you:

 

4=(-2)*1/2+b or b=5.

 

This means your final equation equals y=1/2x+5 

Answer 2

ok so we know that the equation is 6x+3y = 2. 

1. We need to write this in the proper y =mx +b format ( 3y= 2 -6x --> y = 2/3 - 2x --> y = -2x + 2/3) 

2. We can see from the equation the slope of this line is -2, and to find the slope of the perpendicular line we need to get the negative reciprocal, which is 1/2 or (1/2, 1) 

3. Now we have to use the y = mx + b and plug and chug to find b. Y = 4, x = -2 , and m = 1/2

4. y = mx +b --> 4 = (1/2) (-2) + b --> 4 = -1+b --> b = 5

5. we have the value of m and b now have to put it into the equation . 

 y = (1/2)x +5

 

 

Answer 3

I would first rearrange the equation so that it is in y=mx+b form:

 

6x+3y=2

Subtract 6x from both sides:

3y=-6x+2 

Divide both sides by 3:

y=-2x+(2/3) 

 

Now we know that the slope of this line is -2 (or -2/1). The slope of a perpendicular line will be the negative reciprocal of the original slope. This means that instead of the slope being -2 (-2/1) the new line with have a slope of 1/2. Now we have the new slope and a point that it goes through, this means that we can use point slope form:

 

y-y₁ = m(x-x₁) the y₁ and x₁ correspond to the coordinate point given in the question.

 

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

Now we simplify - Get rid of the negatives

y-4 = 1/2 (x+2) 

Distribute the 1/2

y-4 = 1/2x +1 

Add 4 to both sides

Y=1/2x +5