Answer:
1) y=⅚x -2⅓
2) y=8/3x -5
Step-by-step explanation:
Point-slope form:
y=mx+c, where m is the gradient and c is the y-intercept.
Parallel lines have the same gradient.
Gradient of given line= [tex] \frac{5}{6} [/tex]
Thus, m=⅚
Susbt. m=⅚ into the equation,
y= ⅚x +c
Since the line passes through the point (4, 1), (4, 1) must satisfy the equation. Thus, substitute (4, 1) into the equation to find c.
When x=4, y=1,
1= ⅚(4) +c
[tex]1 = \frac{20}{6} + c \\ c = 1 - \frac{20}{6} \\ c = 1 - 3 \frac{1}{3} \\ c = - 2 \frac{1}{3} [/tex]
Thus the equation of the line is [tex]y = \frac{5}{6} x - 2 \frac{1}{3} [/tex].
The gradients of perpendicular lines= -1.
Gradient of given line= -⅜
-⅜(gradient of line)= -1
gradient of line
= -1 ÷ (-⅜)
= -1 ×(-8/3)
= [tex] \frac{8}{3} [/tex]
[tex]y = \frac{8}{3} x + c[/tex]
When x=3, y=3,
[tex]3 = \frac{8}{3} (3) + c \\ 3 = 8 + c \\ c = 3 - 8 \\ c = - 5[/tex]
Thus the equation of the line is [tex]y = \frac{8}{3} x - 5[/tex].
