Question

Write the equation of a line that passes through the given point and is parallel to the given line.

1. (-1,3); y = 2x+2

2. (18,2); 3y-x =- 12

Show steps for both problems - 60 points

Answer 1

1. y=2x+5
2. y= 1/3x -4

Explanation:

1.

`(1,-3)=(x_1,y_1)\\\\y =2x+2\\\\m = 2`

Substitute values into point-slope form

`y-y_1=m(x-x_1)\\\\y -3 =2(x-(-1))\\\\y-3=2(x+1)\\\\y-3=2x+2\\\\y=2x+2+3\\\\y=2x+5`

2.

`(18,2) =(x_1,y_1)\\\\3y-x=-12`

Arrange equation in slope-intercept form (y=mx+b)and derive slope

`3y =x-12\\\\(3y)/(3) =(1x)/(3) -(12)/(3) \\\\y = (1)/(3) x -4\\\\m = (1)/(3)`

Substitute values into point-slope form

`y-y_1=m(x-x_1)\\\\\\y-2=(1)/(3) (x-18)\\\\y-2=(1)/(3) x -6\\\\y=(1)/(3) x -6+2\\\\y=(1)/(3) x -4`