Question

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

Answer 1

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.

Answer 2

Answer:

C. 5x+1

Step-by-step explanation:

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