Answer:
3) [tex]y=\dfrac35x+\dfrac25[/tex]
4) a) [tex]y=-2x+7[/tex]
b) [tex]y=\dfrac12x+\dfrac92[/tex]
Step-by-step explanation:
Exercise 3
[tex]-3x + 5y = 2[/tex]
[tex]\implies 5y = 3x + 2[/tex]
[tex]\implies y=\dfrac35x+\dfrac25[/tex]
Exercise 4
a) If L2 is parallel to L1, it has the same slope (gradient) ⇒ [tex]m = -2[/tex]
If L2 passes through point (3, 1):
[tex]y-y_1=m(x-x_1)[/tex]
[tex]\implies y-1=-2(x-3)[/tex]
[tex]\implies y=-2x+7[/tex]
So L2 = L1
b) If L3 is perpendicular to L1, then the slope of L3 is the negative reciprocals of the slope of L1 ⇒ [tex]m = \dfrac12[/tex]
If L3 passes through point (-5, 2):
[tex]y-y_1=m(x-x_1)[/tex]
[tex]\implies y-2=\dfrac12(x+5)[/tex]
[tex]\implies y=\dfrac12x+\dfrac92[/tex]
