perpendicular and parallel lines

Equation of a linear function

Parallel and Perpendicular Lines

Find the equation of a Linear Function y in STANDARD FORM and SLOPE-

INTERCEPT FORM whose graph satisfies the given conditions:

1.Passes through (2,-3) and parallel to the line 3x+4y =2.

Solution:

1. The line 3x+4y=2 in slope-intercept form is

3x+4y=2 4y=-3x+2

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

Its slope is -3/4. Any parallel to it has the slope -3/4. The equation of the line with slope -3/4 and passes through (2,-3) is

y-(-3)=-3/4(x-2) y+3=-3/4(x-2) 4y+12=-3(x-2) 4y+12=-3x+6 4y=-3x-6

y=-3/4x-3/2 or 3x+4y=-6

2. Passes through (-3,2) and perpendicular to the line 4x-3y=2

Solution:

1. The line 4x-3y=2 in slope-intercept form is

4x-3y=2 -3y=-4x+2

y=4/3x-2/3

Its slope is 4/3. Any line perpendicular to it has the slope 4/3. Hence, the required slope -3/4. the equation of the line with the slope -3/4 and passes through (-3,2) is

y-2=-3/4[(x-(-3)] y-2=-3/4(x+3) 4y-8=-3(x+3) 4y-8=-3x-9 4y=-3x-1

y=-3/4x-1/4 or 3x+4y=-1

Find the equation of the Linear Function y in slope-Intercept form and in Standard form satisfying the given

conditions1. Parallel to the line x+y=2, passing through (-1,2)2. Parallel to the line 3x+4y=12, passing through (0,-2)3. Perpendicular to the line x+y=3, passing through (-

4,3)4. Perpendicular to the line 2x-3y=6, passing through

(3,-4)

No Assignment