Write the equation of a line in Slope Intercept Form that passes through (−2,5) and (3,15).

Mathematics

1 answer:

Inessa [10]2 years ago

8 0

Answer:

$\displaystyle y = 2x + 9$

Step-by-step explanation:

First, find the rate of change [slope]:

$\displaystyle \frac{-y_1 + y_2}{-x_1 + x_2} = m \\ \\ \frac{-5 + 15}{2 + 3} = \frac{10}{5} = 2$

Then, plug the coordinates into the Slope-Intercept Formula instead of the Point-Slope Formula because since you get it done much faster that way. It does not matter which ordered pair you choose:

15 = 2[3] + b

$\displaystyle 9 = b \\ \\ y = 2x + 9$

_______________________________________________

5 = 2[−2] + b

−4

$\displaystyle 9 = b \\ \\ y = 2x + 9$

** You see? I told you it did not matter which ordered pair you choose because you will always get the exact same result.

I am joyous to assist you anytime.

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A rope from the top of a pole is anchored to the ground which is 55 ft away from the base of the pole. The pole is 48 ft tall. W

Irina-Kira [14]

Answer:

73 feet.

Step-by-step explanation:

Given:

A rope from the top of a pole is anchored to the ground which is 55 ft away from the base of the pole.

The pole is 48 ft tall.

Question asked:

What is the length of the rope?

Solution:

Here we found that a right angle triangle is formed in which base and height is given as shown in the figure, we have to find the longest side of the triangle,

Base = 55 feet

Height = 48 feet

Length of the rope = ?

By Pythagoras theorem:

Square of longest side = Square of base + Square of height

$(Longest\ side)^{2} =$ $55^{2} +48^{2}$