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emmainna [20.7K]
2 years ago
7

Slope (12,-7) and (4,5)

Mathematics
1 answer:
Setler79 [48]2 years ago
6 0

(\stackrel{x_1}{12}~,~\stackrel{y_1}{-7})\qquad (\stackrel{x_2}{4}~,~\stackrel{y_2}{5}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{5}-\stackrel{y1}{(-7)}}}{\underset{run} {\underset{x_2}{4}-\underset{x_1}{12}}}\implies \cfrac{5+7}{-8}\implies \cfrac{12}{-8}\implies -\cfrac{3}{2}

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A line's y-intercept is -10, and its slope is 1. What is its equation in slope-intercept form?
ratelena [41]

Answer:

y=1x-10

Step-by-step explanation:

y=mx+b

m(slope) = 1

b(y-intercept) = -10

y=1x-10

✨Hope this helps✨

5 0
3 years ago
29+10j= -11<br> Find the value for j
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<span>29+10j= -11
</span><span>29+10j - 29 = -11 - 29 (subtract 29 to both sides)
10j = -40
10j/10 = -40/10 (divide both sides by 10)
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3 years ago
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Andre45 [30]

Answer:

$1.78

Step-by-step explanation:

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3 years ago
What is the justification for the step taken from line 2 to line 3?
stiv31 [10]

Step-by-step explanation:

3x+9-7x=x+10+x\\-4x+9=2x+10\\-6x+9=10\\

  • In the line 2, only variables were operated with a reduction of similar terms in each side of the equation, giving as result -4x at one side, and 2x at the other side.
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Given points A(-1, -2) and B(2, 4) where AP: BP=1:2, find the locus of point P.​
koban [17]

Answer:

x^2 + 4x + y^2 +8y  =  0

Step-by-step explanation:

Given

A = (-1,-2)

B = (2,4)

AP:BP = 1 : 2

Required

The locus of P

AP:BP = 1 : 2

Express as fraction

\frac{AP}{BP} = \frac{1}{2}

Cross multiply

2AP = BP

Calculate AP and BP using the following distance formula:

d = \sqrt{(x - x_1)^2 + (y - y_1)^2}

So, we have:

2 * \sqrt{(x - -1)^2 + (y - -2)^2} = \sqrt{(x - 2)^2 + (y - 4)^2}

2 * \sqrt{(x +1)^2 + (y +2)^2} = \sqrt{(x - 2)^2 + (y - 4)^2}

Take square of both sides

4 * [(x +1)^2 + (y +2)^2] = (x - 2)^2 + (y - 4)^2

Evaluate all squares

4 * [x^2 + 2x + 1 + y^2 +4y + 4] = x^2 - 4x + 4 + y^2 - 8y + 16

Collect and evaluate like terms

4 * [x^2 + 2x + y^2 +4y + 5] = x^2 - 4x + y^2 - 8y + 20

Open brackets

4x^2 + 8x + 4y^2 +16y + 20 = x^2 - 4x + y^2 - 8y + 20

Collect like terms

4x^2 - x^2 + 8x + 4x + 4y^2 -y^2 +16y + 8y  + 20 - 20 =  0

3x^2 + 12x + 3y^2 +24y  =  0

Divide through by 3

x^2 + 4x + y^2 +8y  =  0

3 0
3 years ago
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