What is the equation of a line that contains the point (2,1) and is perpendicular to the line: y = 3x – 4?

1 answer:

8 0

Y = 3x - 4.....the slope here is 3. A perpendicular line will have a negative reciprocal slope. To find the negative reciprocal, u flip the slope and change the sign. So we will need a slope of -1/3...see how I flipped the slope of 3/1 and made it 1/3...and then changed the sign, making it -1/3.

y = mx + b
slope(m) = -1/3
(2,1)...x = 2 and y = 1
now we sub and find b, the y int
1 = -1/3(2) + b
1 = -2/3 + b
1 + 2/3 = b
3/3 + 2/3 = b
5/3 = b

so ur perpendicular equation is : y = -1/3x + 5/3

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Through: (-3,0), perp. to y = 3x - 1

Marrrta [24]

Answer:

$y=-\dfrac{1}{3}x-1$

Step-by-step explanation:

Given:

line y=3x-1

point (-3,0)

Write: equation of the line that is perpendicular to the given and passes through the point (-3,0)

Solution:

The slope of the given line is $m=3$

If $m_1$ is the slope of perpendicular line, then

$m\cdot m_1=-1\\ \\3m_1=-1\\ \\m_1=-\dfrac{1}{3}$

So, the equation of the needed line is $y=-\dfrac{1}{3}x+b.$

Find b. This line passes through the point (-3,0), so its coordinates satisfy the equation:

$0=-\dfrac{1}{3}\cdot (-3)+b\\ \\0=1+b\\ \\b=-1\\ \\y=-\dfrac{1}{3}x-1$

7 0

3 years ago

Need help on this! Please someone help!!!

Jet001 [13]

This can be easily solved, especially with a calculator.
With the calculator, you can find that $\sqrt{42}$ is about 6.4807.
Multiply that by 2, you get about 13 inches.

If you can't use a calculator, then you can just estimate. Since we know that $\sqrt{36}$ is 6 and $\sqrt{49}$ is 7, $\sqrt{42}$ is in between them, so you can just say somewhere around 6.5.

Multiply 2 * 6.5 and you get 13 inches.