Question

1) Find an equation for the given line in the form ax+by=c, where a, b, and c are integers with no factor common to all three and a≥0.

Through (-40,35) parallel to 7x+8x=19

The equation of the line in the form ax+by=c passing through (-40,35) and parallel to 7x+8x=19 is what?

2) Write an equation in standard form for the line described.

Through (3,8) perpendicular to 5x+y=7

Show Work**

Answer 1

Sol:

equation parallel to line ax+by+c=0 is of the form ax+by+k=0

given line is

7x+8y-19=0

for this line parallel line is 7x+8y-k=0

this passes through

7*(-40)+8*35+k=0

k=0

therefore equation of line parallel to 7x+8x=19 is 7x+8y=0

ANSWER:

parallel line to given line is 7x+8y=0

Solution2:

equation of line perpendicular to ax+by+c=0 is bx-ay+k=0

line perpendicular to 5x+y-7=0 is x-5y+k=0

this passes through (3,8)

3-5*8+k=0

-37+k=0

k=37

the perpendicular line to 5x+y-7=0 is x-5y+37=0

ANSWER:

perpendicular line to given line is x-5y+37=0