Question

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

Answer 1

Answer:

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

Step-by-step 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

$3y =x-12\\\\\frac{3y}{3} =\frac{1x}{3} -\frac{12}{3} \\\\y = \frac{1}{3} x -4\\\\m = \frac{1}{3}$

Substitute values into point-slope form

$y-y_1=m(x-x_1)\\\\\\y-2=\frac{1}{3} (x-18)\\\\y-2=\frac{1}{3} x -6\\\\y=\frac{1}{3} x -6+2\\\\y=\frac{1}{3} x -4$