Write the equation of the line through (-1,4) with slope m=2/3 in standard form (Ax+By=C)

Question

Standard form ( Ax + By = C )

Answer 1

Sofia,

 

For this problem, you are given the slope and a point, and need to find c (which is b in the slope intercept form).

 

I prefer to use slope intercept, so I would solve for b in this equation:

4=2/3(-1)+b

4=-2/3+b

4+2/3=b

12/3+2/3=b

14/3=b

 

Now substitute into equation:

y=2/3(x)+14/3

 

Write in standard form:

-2/3(x)+y=14/3

 

Multiple entire equation by 3 to eliminate the fraction:

[-2/3(x)+y=14/3]3

-2x+3y=14

 

I hope that helps.

 

Norm.

Answer 2

OK, first I would put this in point-slope. y-y₁=m(x-x₁)

 

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

 

Then, take it to slope intercept.y=mx+b

 

y-4=(2/3)(x+1)  Add 4 to both sides to get y=(2/3)x +5. 

Now I would go to standard form.

 

Subtract the slope from both sides. You get (-2/3)x+y=5. If you want to get rid of the fraction, multiply the equation by 3 and get -2x+3y=15. 

 

 

[[EDIT ---  Sorry, I didn't distribute the (2/3) while I was in slope-intercept! So do that and get y-4 =(2/3)x +(2/3) before adding 4. You'll end up with y=(2/3)+(14/3) and you can go to standard form from there.]]

Answer 3

I got  a different answer so I will present it just in case. My apologies if I am wrong.

 

 

Here it goes....

 

English: write slope intercept format

Math:

y = mx + b

 

English: Label given information

Math: 

m = 2/3; (-1,4) x = -1 and y = 4

 

English: substitute given information into slope intercept format and solve for b

Math:

4 = (2/3)(-1) + b

4 = -2/3 + b                       evaluate

4 + 2/3 = -2/3 + 2/3 + b    add 2/3 to each side

12/3 + 2/3 = b

14/3 = b

 

English: write equation of the line in y = mx + b format

Math:

y = (2/3)x + (14/3)

 

English: rewrite equation in Ax + By = C format (Note: eliminate all fractions from answer)

Math:

y - (2/3)x = (2/3)x - (2/3)x + (14/3)       subtract (2/3)x from each side

-(2/3)x + y = (14/3)                               

(-3)(-2/3)x + y(-3) = (14/3)(-3)             multiply each term by -3 to get rid of fraction

2x - 3y = -14

 

English: write answer

 

2x - 3y = -14

 

 

 

Answer 4

(y-4)/(x+1) = 2/3
3(y-4) = 2(x+1)
3y -12 = 2x + 2
3y -2x = 14

or

4 = 2(-1)/3 + b, 4 +2/3 = b

=> b = 14/3

y = 2/3x + 14/3

(y = 2/3x + 14/3) * 3   multiplying through by 3

3y = 2x + 14

<=> 3y -2x = 14

 

Answer 5

use the point-slope form or the slope-intercept form

y=mx+b

y=(2/3)x+b

4=(2/3)(-1)+b

4=(-2/3)+b

4+(2/3)=b

(14/3)=b

y=(2/3)x+(14/3)

multiply both sides by 3

3y=2x+14

-2x+3y=14, or...

2x-3y=-14