write the equation of the line in standard form that passes through (-5,-11) and (10,7)

Question

Write the equation of the line in standard form the passes through (-5.-11) and (10,7)

Answer 1

Say the points (x1,y1) = (-5,-11)

(x2,y2) = (10,7)

Line equation to through the points is y-y1 = [(y2-y1)/(x2-x1)](x-x1)

y+11 = [(7+11)/(10+5)](x+5)

y+11 = (18/15)(x+5)

Cross multiplication.

15y+165 = 18x+90

Subtract 165 to each side.

15y+165-165 = 12x+90-165

15y = 12x-75

Divide to each side by 15.

15y/15 = 12x/15-75/15

y = 4/5x-5

Comments

Line equation is wrong since slope is wrong

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

= (7 -( -11)) / ( 10 - ( -5))

= 18 / 15

= 6/ 5

Answer 2

The standard form of a line is in the form Ax + By = C where A is a positive integer, and B, and C are integers.

The line equation is y = mx + b

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

= (7 -( -11)) / ( 10 - ( -5))

= 18 / 15

= 6/ 5

Line equatio is y = 6/5x + b

Find y-intercept by substituing any point on the line  say (10, 7)

7 = 6/5 * 10 + b

b = -5

The line equation is y = 6/5 x - 5

Eliminate fractions by multiplying the equation by 5

5y = 6x - 25

Subtract 5y from each side

6x - 5y - 25 = 0

Add 25 to each side

6x - 5y = 25

The standard form line equation is 6x - 5y = 25