What is the equation of the line that is perpendicular to and has the same y-intercept as the given line?

Mathematics

2 answers:

Anastasy [175]3 years ago

8 0

ANSWER

The required equation is

$y = 5x + 1$

EXPLANATION

The given line passes through the point

$(5,0) \: and \: (0,1)$

The slope of this line is given by the formula,

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

This implies that,

$m = \frac{1 - 0}{0 - 5}$

$m = - \frac{1}{5}$

The product of the slope of the two perpendicular lines should be negative one.

Thus,

$m_1\times m_2=-1$
This implies that,

$- \frac{1}{5} \times m_2=-1$

We multiply through by
$- 5$
to obtain,

$m_2=-1 \times - 5$

$m_2=5$
Therefore the slope of the line perpendicular to the given line is
$5.$

We use the slope intercept formula
$y =m x + b$

where
$b = 1$
is the y-value of the y-intercept.

We therefore have,

$y = 5x + 1$

as the required equation.

The correct answer is C.

Anestetic [448]3 years ago

8 0

Answer:

C. 5x+1

Step-by-step explanation:

edge2020

You might be interested in

The probability mass function of X is f(x)= 1/6, x 1.2...,6 then find out the value

Mumz [18]

For the given probability mass function of X, the mean is 3.5 and the standard deviation is 1.708.

A discrete random variable X's probability mass function (PMF) is a function over its sample space that estimates the likelihood that X will have a given value. f(x)=P[X=x].
The total of all potential values for a random variable X, weighted by their relative probabilities, is known as the mean (or expected value E[X]) of that variable.
Mean(μ) = 1(1/6) + 2(1/6) + 3(1/6) + 4(1/6) + 5(1/6) + 6(1/6).
Mean(μ) = (1+2+3+4+5+6)/6
Mean(μ) = 21/6
Mean(μ) = 3.5
The square root of the variance of a random variable, sample, statistical population, data collection, or probability distribution represents its standard deviation. It is denoted by 'σ'.
A random variable's variance (or Var[X]) is a measurement of the range of potential values. It is, by definition, the squared expectation of the distance between X and μ. It is denoted by 'σ²'.
σ² = E[X²]−μ²
σ² = [1²(1/6) + 2²(1/6) + 3²(1/6) + 4²(1/6) + 5²(1/6) + 6²(1/6)] - (3.5)²
σ² = [(1² + 2²+ 3² + 4²+ 5²+ 6²)/6] - (3.5)²
σ² = [(1 + 4 + 9 + 16 + 25 + 36)/6] - (3.5)²
σ² = (91/6) - (3.5)²
σ² = 15.167-12.25
σ² = 2.917
σ = √2.917
Standard deviation (σ) = 1.708