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

3)
`y=\frac35x+\frac25`

4) a)
`y=-2x+7`

b)
`y=\frac12x+\frac92`

Explanation:

Exercise 3

`-3x + 5y = 2`

`\implies 5y = 3x + 2`

`\implies y=\frac35x+\frac25`

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 = \frac12`

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

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

`\implies y-2=\frac12(x+5)`

`\implies y=\frac12x+\frac92`