Write the equation of the line with the following characteristics

Question

Write the equation of the line with the following characteristics

a) passes through (3, -4) and (5, 2)

b) is a horizontal line with a y-intercept at -4

c) is a vertical line that passes through (7, -8)

d) has an x-intercept at 5 and a y-intercept at -3

e) is parallel to the line 3𝑥 + 4𝑦 = 7, passes through the point (-6, 4) and is written in

point-slope form

f) is perpendicular to the line 5𝑥 − 3𝑦 = 0, passes through the point (4 , 8) and is written in point-slope form

show works

Answer 1

a)

M = (-4 -2)/(3-5) = -6/-2 = 3

B = y - mx = 2 - 3*5 = -13

y = 3x-13

(b) y=-4

(c) x=7

(d) the intercepts are (5,0) and (0,-3)

then M = (-3-0)/(0-5) = 3/5

B = y - mx = -3 - (3/5)(0) = -3

y = (3/5)x - 3

(e)

3x+4y = 7

4y = -3x+7

y = (-3/4)x + 7/4

the parallel line has slope -3/4

B = y - mx = 4 - (-3/4)(-6)

= 4 - (18/4)

= 16/4 - 18/4

= -2/4

= -1/2

y = (-3/4)x - 1/2

sorry , you want point slope form...

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

(f) 5x-3y = 0

5x = 3y

(5/3)x = y

the perpendicular line has slope -3/5

B = y - mx

= 8 - (-3/5)(4)

= 8 + 12/5

= 40/5 + 12/5

= 52/5

y = (-3/5)x + 52/5

oops, i did it again, you want point slope form..

y-8 = (-3/5)(x-4)