Question

Please help me with these please.

Answer 1

6. Answer: y = 5x - 11

Step-by-step explanation:

Parallel means "same slope".  y = 5x - 2 is in the form y = mx + b,

so the slope (m) = 5

Next, input the point (x₁, y₁ = 2, -1) and slope (m = 5) into the Point-Slope formula:

y - y₁ = m(x - x₁)

y - (-1) = 5(x - 2)

y + 1 = 5x - 10

y      = 5x - 11

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7. Answer: $\bold{y = \dfrac{1}{3}x + 4}$

Step-by-step explanation:

Perpendicular means "opposite reciprocal slope". y = -3x + 7 is in the form y = mx + b, so slope (m) = -3 ⇒ m⊥ = $\frac{1}{3}$

Next, input the point (x₁, y₁ = 3, 5) and slope (m = $\frac{1}{3}$ ) into the Point-Slope formula:

y - y₁ = m(x - x₁)

$y - 5=\dfrac{1}{3}(x - 3)$

$y - 5 =\dfrac{1}{3}x - 1$

   $y=\dfrac{1}{3}x + 4$