Question

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Answer 1

Explanation:

1) (-6 , 2) ; (3 , -5)

Slope = \frac{y_{2}-y_{1}}{x_{2}-x_{1}}

x

2

−x

1

y

2

−y

1

\begin{gathered}= \frac{-5-2}{3-[-6]}\\\\= \frac{-5-2}{3+6}\\\\= \frac{-7}{9}\\\end{gathered}

=

3−[−6]

−5−2

=

3+6

−5−2

=

9

−7

m = -7/9 ; (-6 , 2)

y - y₁ = m(x -x₁)

y - 2 = (-7/9)(x - [-6])

Answer 2

Explanation:

1) (-6 , 2) ; (3 , -5)

Slope =
`(y_(2)-y_(1))/(x_(2)-x_(1))`

`= (-5-2)/(3-[-6])\\\\= (-5-2)/(3+6)\\\\= (-7)/(9)\\`

m = -7/9 ; (-6 , 2)

y - y₁ = m(x -x₁)

y - 2 = (-7/9)(x - [-6])

`y - 2 = (-7)/(9)(x + 6)\\\\y -2 = (-7)/(9)x + (-7)/(9)*6\\\\y - 2 = (-7)/(9)x - (7*2)/(3)\\\\ y = (-7)/(9)x - (14)/(3) + 2\\\\y = (-7)/(9)x -(14)/(3) + (2*3)/(1*3)\\\\y = (-7)/(9)x - (14)/(3) + (6)/(3)\\\\y = (-7)/(9)x - (8)/(3)`

2) (3 , -4) ; m= 3

`y - y_(1) = m(x - x_(1)`)

y - [-4] = 3(x - 3)

y + 4 = 3x - 3*3

y + 4 = 3x - 9

y = 3x - 9 - 4

Ans: y = 3x - 13

3) m = 2 ; y-intercept (b) = 3/2

y = mx + b

Ans: y = 2x + (3/2)

4) (-1, 3 ) ; (2 , 0)

Slope =
`(0 - 3)/(2-[-1])`

`= (-3)/(2+1)\\\\= (-3)/(3)\\\\= 1`

m = 1; ( -1 , 3)

y - 3 = 1(x -[-1])

y - 3 = 1(x + 1)

y - 3 = x + 1

y = x + 1 + 3

Ans: y = x + 4

5)(2, 1) ;m = -3

y - 1 = (-3)(x - 2)

y - 1 = -3x + 6

y = -3x + 6 +1

Ans: y = -3x + 7