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4vir4ik [10]
2 years ago
6

Write the equation of the line passing through the points (-4,-1) and (2,8)

Mathematics
1 answer:
klio [65]2 years ago
7 0
<h3><u>Explanation</u><u>:</u></h3>
  • Calculate the slope with two given coordinate points by using rise over run.

m =  \frac{y_2 - y_1}{x_2 - x_1}

Let these points

\begin{cases}(x_1, y_1) = ( - 4,  - 1) \\ (x_2, y_2) = ( 2,  8) \end{cases}

m =  \frac{8 - ( - 1)}{2 - ( - 4)}  \\ m =  \frac{8 + 1}{2 + 4}  \Longrightarrow \frac{9}{6}  \Longrightarrow \frac{3}{2}  \\ m =  \frac{3}{2}

  • Slope-Intercept

y = mx + b \\ m = slope \\ b = y - intercept

Substitute the value of m in the equation.

y =  \frac{3}{2} x + b

  • Substitute any coordinate points that are given or part of the graph in the equation.

(x_, y) = ( - 4,  - 1)

- 1 =  \frac{3}{2} ( - 4) + b

  • Solve the equation for b-term.

- 1 =  \frac{3}{ \cancel{2}} ( \cancel{ - 4})   + b\\  - 1 = 3( - 2) + b \\  - 1 =  - 6 + b \\  - 1 + 6 = b \\ 5 = b

  • Rewrite the equation by substituting the value of b in the equation.

y =  \frac{3}{2} x + 5

<h3><u>Answer</u></h3>

\large \boxed{y =  \frac{3}{2} x + 5}

<em>If</em><em> </em><em>you</em><em> </em><em>have</em><em> </em><em>any</em><em> </em><em>questions</em><em> </em><em>related</em><em> </em><em>to</em><em> </em><em>the</em><em> </em><em>answer</em><em>,</em><em> </em><em>feel</em><em> </em><em>free</em><em> </em><em>to</em><em> </em><em>ask</em><em> </em><em>via</em><em> </em><em>comment</em><em>.</em>

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Answer:

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Step-by-step explanation:

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6 0
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Question 1
Alexxx [7]

Answer:

Water needed for pool = 486 cubic feet

Plastic liner required for the pool = 298.3 feet

Step-by-step explanation:

Top view of the pool is a composite figure, having one rectangle and a trapezoid.

1). Water needed for the pool = volume of the pool

Volume of the pool = Area of the base × Depth

                               = (Area of the rectangle + Area of the trapezoid)× depth  

Area of the trapezoid = \frac{1}{2}(b_{1}+b_{2})\times h

                                    = \frac{1}{2}(11+9)\times (12-1.5)

                                    = 105 ft²

Area of the rectangle = Length × width

                                    = 11 × 1.5

                                    = 16.5 ft²

Now, volume of the pool = (105 + 16.5) × 4

                                          = 121.5 × 4

                                          = 486 cubic feet

b). Liner required = surface area of the pool excluding top

                             = Surface area of the walls + Area of the pool base

                             = (Perimeter of the pool) × depth + area of the base

                             = (12 + 11 + 1.5 + 10.7 + 9)×4 + 121.5

                             = 176.8 + 121.5

                             = 298.3 square feet

Therefore, amount of water required = 486 cubic feet

liner needed = 298.3 square feet                                  

8 0
2 years ago
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