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3 years ago

(3,4) and (12,19) find the equation of the line that passes through it

Mathematics

1 answer:

harina [27]3 years ago

5 0

Answer:

The equation of the line will be:

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

Step-by-step explanation:

Given the points

(3, 4)

(12, 9)

Finding the slope between (3, 4) and (12, 9)

$\left(x_1,\:y_1\right)=\left(3,\:4\right),\:\left(x_2,\:y_2\right)=\left(12,\:19\right)$

$\mathrm{Slope}=\frac{y_2-y_1}{x_2-x_1}$

$m=\frac{19-4}{12-3}$

$m=\frac{5}{3}$

The equation of the line can be obtained using the point-slope form of the equation of the line

$y-y_1=m\left(x-x_1\right)$

substituting the values m = 5/9 and the point (3, 4)

$y-4=\frac{5}{3}\left(x-3\right)$

$y-4+4=\frac{5}{3}\left(x-3\right)+4$

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

Therefore, the equation of the line will be:

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

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3 years ago

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Vera_Pavlovna [14]

We can solve by figuring the area of the rectangle then add it to the area of the semicircle.

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3 years ago

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Figure ABCDE has vertices a(-3, 3), b(2, 3), c(5, -2), d(0, -3), and e(-3, -2). Plot the points on your own coordinates grid and

Ilya [14]

<h2>Answer:</h2>

Shown below

<h2>Step-by-step explanation:</h2>

First of all, we have the following points:

$a(-3, 3) \\ \\ b(2, 3) \\ \\ c(5, -2) \\ \\ d(0, -3) \\ \\ e(-3, -2)$

To plot these points, we need to graph a coordinate grid. Recall that a coordinate grid is composed of two perpendicular lines, that we call the axes and are labeled like number lines. The horizontal axis is called the x-axis while the vertical axis is called the y-axis, and these two axes intersect at a point called the origin. Next, let's plot each point as follows:

<h2>PART 1. Plot the points on your own coordinates grid and connect in alphabetical order. </h2><h2></h2>

Point a:

Let's stand at the origin and then move three units to the left and three units up. The resulting point is shown in the firs figure below.

Point b:

Let's stand at the origin and then move two units to the right and three units up. The resulting point is shown in the firs figure below.

Point c:

Let's stand at the origin and then move five units to the right and two units down. The resulting point is shown in the firs figure below.

Point d:

Let's stand at the origin and then move three units to down. The resulting point is shown in the firs figure below.

Point e:

Let's stand at the origin and then move three units to the left and two units down. The resulting point is shown in the firs figure below.

Next, let's connect connect the points in alphabetical order, so that the line are connected from a to b, from b to c, from c to d, from d to e and from e to a again. So the resulting graph is shown in the second figure. As you can see, this is an irregular pentagon.

<h2>PART 2. Decompose figure ABCDE into rectangles and triangles.</h2>

Every pentagon can be divided up into three triangles. Hence, from the third figure. the triangles are:

ΔABE

ΔBDE

ΔBCD

Since a rectangle is a quadrilateral whose angles are all right angles, then there is no chance to obtain a rectangle from ABCDE. To obtain a rectangle, we'd need other points and this is not what the problem asks.

5 0

3 years ago

X= <br> Y=<br> Find the values of X and Y

Art [367]

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

x = 50°
y = 65°

<h3><u>Step-by-step explanation:</u></h3>

<u>We can clearly see that the triangle is an isosceles triangle. This also means that y must equal to 180 - 115. Let's solve.</u>

=> x + y + 180 - 115 = 180
=> x + y + 65 = 180

<u>Since 180 - 115 equals 65, this means that </u><u>y = 65.</u>

=> x + 65 + 65 = 180
=> x + 130 = 180
=> x = 180 - 130
=> x = 50

<h3><u>Conclusion:</u></h3>

<u>Therefore, our answers are:</u>

x = 50°
y = 65°

Hoped this helped.

$-BrainiacUser1357-$

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2 years ago