An equation for a line passing thru (1, 2) and (4, 6) is?

Question

4x - 3y + 2 = 0

possible solutions....

4x + 3y - 2 = 0

4x + 3y + 2 = 0

4x - 3y - 2 = 0

Answer 1

Step 1: find the slope using the slope formula.

m = (y2 - y1) / (x2 - x1)

(x1,y1) = (1, 2)
(x2,y2) = (4, 6)

m = (6 - 2) / (4 - 1) = 4/3

Step 2: Now that we have the slope, reuse the slope formula to get the equation of the line. This time, use (1, 2) and (x, y) as (x1, y1) and (x2, y2)

(y2 - y1) / (x2 - x1) = m

But the difference is, we have the slope now. m = 4/3.

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

Cross multiplying,

3(y - 2) = 4(x - 1)
3y - 6 = 4x - 4

Moving everything over to the right hand side,

0 = 4x - 3y + 2

Answer 2

An equation for a line passing thru (1, 2) and (4, 6) is
(y-y1)/(x-x1) = (y2-y1)/x2-x1)
(y-2)/(x-1) = (6-2)/(4-1) = 4/3
y-2= 4/3(x-1)
y = 4/3x-4/3+2 = 4x/3-2/3
3y = 4x -2
4x-3y -2 = 0

Answer 3

By using the formula: (y-y1)/(y2-y1)=(x-x1)/(x2-x1)
y-2/6-2=x-1/4-1
y-2/4 =x-1/3
3y-6 =4x-4
4x-3y+2=0

Answer 4

The slope m of the line: m = distinction in Y-coordinates/ distinction of X-coordinates =(-2+6)/(one million-4) = - 4/3. The equation of the line is y-b =m(x-a). right here, y+2 = (- 4/3)(x-one million) Or 3y +6 = - 4x +4. which leads to : 4x+3y +2 =0. answer. ensure: ok

Answer 5

y=mx+b

m=rise/run = (6-2)/(4-1) = 4/3
so y = 4/3x + b
Plug in values of x and y from one of the points (1,2):
2 = 4/3(1)+b
b=2-4/3 = 2/3

y = 4/3x + 2/3
multiply by 3:
3y = 4x + 2
so
0 = 4x - 3y + 2

Answer 6

y=mx+b

m=slope=rise/run

rise=6-2=4
run=4-1=3
m=4/3

now use y=mx+b to find b
(4,6)
6=(4/3)(4)+b
6=16/3+b
18/3-16/3=b
2/3=b
y=(4/3)x+(2/3)

To choose between the options, you need to remove the fraction which you can do by multiplying all the terms by 3

3(y)=(3)(4/3)x+(3)(2/3)
3y=4x+2
4x-3y+2=0

Answer 7

using two point formula,

(y-y1)/(x-x1)= (y2-y1)/(x2-x1)

assume y1=2 ;x1 =1; y2=6; x2=4

(y-2)/(x-1)=(6-2)/(4-1)
(y-2)/(x-1)= 4/3
3y-6 = 4x-4
4x-3y-2=0

Ans: Equation of line is 4x-3y-2=0