equation of the line please help1

Question

 

equation of the line

1) write an equation of the line parallel  to x+2y=6 through (8,3) 2) find the equation of a line containing points (-2,8) and (3,5) 3) write an equation of the line parallel  to y=3x-2 through (1,-3) 4) write an equation of the line parallel  to x+y=-3 through (0,4) 5) write an equation of the line parallel  to 2x-y=1 through (-1,2) 6) write an equation of the line parallel  to x-y=-4 through (1,-3)

 

Answer 1

2.

Given points  are (-2, 8) and (3, 5).

The line passes through (x1,y1) = (-2,8) and (x2,y2) = (3,5). Find its slope.

m = y2 - y1/x2 - x1 = 5 - 8/3 -(-2)

Product of two same signs is positive.

m = -3/5

You know the slope and a point on the line, so use the point - slope form with either given point to  to write  equation of the line.

Choose (x1,y1) = (3,5)

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

(y - 5) = -3/5(x - 3)

5(y-5) = -3(x-3)

Apply distributive property: a(b - c) = ab - ac.

5y -25 = -3x + 9

Add 25 to each side.

5y - 25 + 25 = -3x + 9 + 25

5y  = -3x + 34

3x+5y-34 = 0

The line equation is 3x+5y-34 = 0