What is the equation of the line that passes through the point (1,3) and has a slope of -- 32

Mathematics

1 answer:

Korolek [52]3 years ago

5 0

Answer:

The equation of the line that passes through the point (1,3) and has a slope of -32.

$y=-32x+35$

Please check the attached graph too.

Step-by-step explanation:

Given

Point (1, 3)

The slope m = -32

The point-slope form:

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

where

m is the slope of the line

(x₁, y₁) is the point

In our case:

m = -32

(x₁, y₁) = (1, 3)

substituting m = -32 and (x₁, y₁) = (1, 3) in the point-slope form of the line equation

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

$y-3=-32\left(x-1\right)$

Add 3 to both sides

$y-3+3=-32\left(x-1\right)+3$

Simplify

$y=-32x+35$

Therefore, the equation of the line that passes through the point (1,3) and has a slope of -32.

$y=-32x+35$

Please check the attached graph too.

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Triangle ABC has sides with lengths of 11, 18, and 8 units. Determine whether this triangle is a right triangle.

Arturiano [62]

Answer:

Not a right triangle.

Step-by-step explanation:

If this triangle is a right triangle, then the Pythagorean theorem would work on it. According to the Pythagorean theorem, $a^2+b^2=c^2$ , so c would always be greater than a or b. In this scenario, the greatest number here is 18, so c = 18. Since a or b don't matter if given both legs, we have the following equation that may or may not be equal: $8^2+11^2=18^2$ . We know 8 squared is 64, and 11 squared is 121, and 18 squared is 324. This means that $64+121=324$ according to the Pythagorean theorem, and since 64 + 121 = 185, and 185 does not equal 324, the Pythagorean theorem does not work and the triangle is not a right triangle.