Question

19 Line a is parallel to line b. Line b passes through the points (-2, 7) and (5, 3) and line a passes through the point (-5, 1). Write an equation of line a in point-slope form.

Answer 1

`y - 1 = - (4)/(7) (x + 5)`

Explanation:

Point-slope form

y- y₁= m(x -x₁), where m is the slope and (x₁, y₁) is a coordinate the line passes through

Parallel lines have the same slope.

`\boxed{slope = (y1 - y2)/(x1 - x2) }`

Slope of line a

= slope of line b

`= (7 - 3)/( - 2 - 5)`

`= (4)/( - 7)`

`= - (4)/(7)`

Substituting the slope into the equation:

`y - y1 = - (4)/(7) (x - x1)`

Substituting the coordinates (-5, 1):

`y - 1 = - ( 4)/(7) [x -( - 5)]`

`y - 1 = - (4)/(7) (x + 5)`