(k, k + 1), (k - 3, 3k + 4), m = 2 in slope- point form

Question

find value of k so that the line passing through the given points has the given  slope. write an equation of the line in point- slope form.

Answer 1

Given two points (x1,y1) = (k,k+1)

(x2,y2) = (k-3,3k+4)

Slope m = y2-y1/x2-x1

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

2 = 3k+4-k-1/-3

2 = 2k+3/-3

Multiple by negitive 3 to each side.

2*-3 =2k+3/-3*-3

-6 =2k+3

Subtract 3 from to each side.

-6-3 = 2k+3-3

-9 = 2k

Divide by 2 to each side.

-9/2 = 2k/2

k = -9/2

Substitute the k value in given points(k, k+1) (k-3, 3k+4)

the points are (-9/2,-9/2+1) (-9/2-3,3*-9/2+4)

(-9/2,-7/2) (-15/2,-19/2)

Equation to the line passes through above points and its slope m =2

y+7/2 = 2(x+9/2)

y+7/2 = 2x+9

y+7 = 4x+36

y =4x+36-7

y = 4x+29

Answer 2

Given two points (x1,y1) = (k,k+1)

(x2,y2) = (k-3,3k+4)

Slope m = y2-y1/x2-x1

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

2 = 3k+4-k-1/-3

2 = 2k+3/-3

Multiple by negitive 3 to each side.

2*-3 =2k+3/-3*-3

-6 =2k+3

Subtract 3 from to each side.

-6-3 = 2k+3-3

-9 = 2k

Divide by 2 to each side.

-9/2 = 2k/2

k = -9/2

Substitute the k value in given points(k, k+1) (k-3, 3k+4)

the points are (-9/2,-9/2+1) (-9/2-3,3*-9/2+4)

(-9/2,-7/2) (-15/2,-19/2)

Equation to the line passes through above points and its slope m =2

y+7/2 = 2(x+9/2)

y+7/2 = 2x+9

Subtract 7/2 from each side.

y+7/2-7/2 =2x+9-7/2

y =2x+11/2

Equation of the line in point slope form y = 2x+11/2

Comments

Point - slope - form - of the line equation is y - y1 = m(x - x1), where m is slope and (x1, y1) is the point lies on the line.

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Point - slope form of line equation is y - y1 = m(x - x1), where m is slope and (x1, y1) is the point lies on the line.

If k = - 9/2 then the points are (- 9/2, - 7/2) and (- 15/2, - 19/2), and slope m = 2.

Use either point for (x 1 , y 1) in the point-slope form.

Method 1 : Use (- 9/2, - 7/2)                                        Method 2 : Use (- 15/2, - 19/2)

y - y1 = m(x - x1).                                                        y - y1 = m(x - x1).

y + 7/2 = 2(x + 9/2)                                                      y + 19/2 = 2(x + 15/2)

The pont - slope form of line equation is y + 7/2 = 2(x + 9/2) (or) y + 19/2= 2 (x + 15/2).