Question

5x+8y=120 line passes 4,5 find parallel

Answer 1

5x + 8y = 60

the equation of a line in ' slope-intercept form ' is

y = mx + c → (m is the slope and c the y-intercept)

rearrange 5x + 8y = 120 into this form

subtract 5x from both sides

8y = - 5x + 120

divide all terms by 8

y = - $\frac{5}{8}$ x + 15 ( in slope-intercept form)

hence slope m = - $\frac{5}{8}$

Parallel lines have equal slopes

thus partial equation is

y = - $\frac{5}{8}$ x + c

to find c substitute (4, 5) into the partial equation

5 = - $\frac{5}{2}$ + c ⇒ c = $\frac{15}{2}$

y = - $\frac{5}{8}$ x + $\frac{15}{2}$

multiply through by 8

8y = - 5x + 60 ⇔ 5x + 8y = 60 → (equation of parallel line)