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Dmitriy789 [7]
2 years ago
6

Please help! Will give brainliest!

Mathematics
1 answer:
const2013 [10]2 years ago
8 0
<h3>1.</h3>

The equation in point-slope form:  y - y₁ = m(x - x₁)

slope:  m = -2

point:   (4, -5)   ⇒   x₁ = 4, y₁ = -5

Therefore, the equation of the line in point-slope form:

<h3>y + 5 = -2(x - 4)</h3>

<h3>2.</h3>

The equation in slope-intercept form:   y = mx + b

Parallel lines has the same slope, so:

y = 4x + 2     ⇒    a = 4

If a line passes through the point <em>(x₁, y₁) </em>then the equation y<em>₁</em> = mx<em>₁</em> + b is true.

(4, 6)  ⇒   x₁ = 4, y₁ = 6  

So:   6 = 4·4 + b  ⇒   b = -10

Therefore the equation:  

<h3>y = 4x - 10</h3>

<h3>3.</h3>

a = 3

(-1, 1)  ⇒   x₁ = -1, y₁ = 1  

So:   1 = 3·(-1) + b  ⇒   b = 4

The equation:  

<h3>y = 3x + 4</h3>

<h3>4. </h3>

The product of slopes of perpendicular lines is -1.

2x - 7y = 1    ⇒  7y = -2x + 1   ⇒  y = -²/₇x + ¹/₇

-²/₇×m = -1    ⇒   m = ⁷/₂

(0, -4)  ⇒   x₁ = 0, y₁ = -4  

-4 = ⁷/₂·0 + b   ⇒   b = -4

The equation:

<h3>y = ⁷/₂x - 4</h3>
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