Question

Y = mx + b to find the equation of the line that passes through the points (−6, 1) and (3, 4).

y = –3x + 5

y = 3x – 5

Answer 1

Answer:

Explanation:

we know that

The equation of the line in slope intercept form is equal to

where

m is the slope

b is the y-coordinate of the y-intercept

we have the points

(−6, 1) and (3, 4)

substitute the value of x and the value of y of each point in the equation of the line, then solve for m and b

For (-6,1)

-----> -----> equation A

For (3,4)

----> -----> equation B

Solve the system of equations A and B

Match equation A and equation B

Solve for m

Find the value of b

The equation of the line is

Explanation:

Answer 2

`y=(1)/(3)x+3`

Explanation:

we know that

The equation of the line in slope intercept form is equal to

`y=mx+b`

where

m is the slope

b is the y-coordinate of the y-intercept

we have the points

(−6, 1) and (3, 4)

substitute the value of x and the value of y of each point in the equation of the line, then solve for m and b

For (-6,1)

`1=-6m+b` ----->
`b=6m+1` -----> equation A

For (3,4)

`4=3m+b` ---->
`b=-3m+4` -----> equation B

Solve the system of equations A and B

Match equation A and equation B

`6m+1=-3m+4`

Solve for m

`6m+3m=4-1`

`9m=3`

`m=(1)/(3)`

Find the value of b

`b=6((1)/(3))+1`

`b=3`

The equation of the line is

`y=(1)/(3)x+3`