Question

Pls help me in these two little exercises about the slope.

Answer 1

#Ex-3

$\\ \tt\rightarrowtail -3x+5y=2$

$\\ \tt\rightarrowtail 5y=2+3x$

$\\ \tt\rightarrowtail y=3/5x+2/5$

#Ex_4(1)

• Line is parallel so slope=3/5
• Passes through (3,1)

Equation in point slope form

$\\ \tt\rightarrowtail y-1=3/5(x-3)$

$\\ \tt\rightarrowtail 5y-5=3x-9$

$\\ \tt\rightarrowtail 3x-5y-4=0$

#2

• Passes through (-5,2)
• Slope=-5/3

$\\ \tt\rightarrowtail y-2=-5/3(x+5)$

$\\ \tt\rightarrowtail 3y-6=-5x-25$

$\\ \tt\rightarrowtail 5x+3y+19=0$

Answer 2

Answer:

3)  $y=\dfrac35x+\dfrac25$

4) a)  $y=-2x+7$

  b)  $y=\dfrac12x+\dfrac92$

Step-by-step explanation:

Exercise 3

$-3x + 5y = 2$

$\implies 5y = 3x + 2$

$\implies y=\dfrac35x+\dfrac25$

Exercise 4

a) If L2 is parallel to L1, it has the same slope (gradient) ⇒ $m = -2$

If L2 passes through point (3, 1):

$y-y_1=m(x-x_1)$

$\implies y-1=-2(x-3)$

$\implies y=-2x+7$

So L2 = L1

b) If L3 is perpendicular to L1, then the slope of L3 is the negative reciprocals of the slope of L1  ⇒  $m = \dfrac12$

If L3 passes through point (-5, 2):

$y-y_1=m(x-x_1)$

$\implies y-2=\dfrac12(x+5)$

$\implies y=\dfrac12x+\dfrac92$