Question

Part ion even know of the hardest test

Answer 1

Given:

The equation of a line is:

$y=-\dfrac{5}{7}x+2$

A line passes through the point (-5,-3) and perpendicular to the given line.

To find:

The equation of the line.

Solution:

Slope intercept form of a line is:

$y=mx+b$                 ...(i)

Where, m is the slope and b is the y-intercept.

We have,

$y=-\dfrac{5}{7}x+2$          ...(ii)

On comparing (i) and (ii), we get

$m=-\dfrac{5}{7}$

We know that the product of slopes of two perpendicular lines is always -1.

$m_1\times m_2=-1$

$-\dfrac{5}{7}\times m_2=-1$

$m_2=\dfrac{7}{5}$

Slope of the required line is $\dfrac{7}{5}$ and it passes through the point (-5,-3). So, the equation of the line is:

$y-y_1=m_2(x-x_1)$

$y-(-3)=\dfrac{7}{5}(x-(-5))$

$y+3=\dfrac{7}{5}(x+5)$

Using distributive property, we get

$y+3=\dfrac{7}{5}(x)+\dfrac{7}{5}(5)$

$y+3=\dfrac{7}{5}x+7$

$y=\dfrac{7}{5}x+7-3$

$y=\dfrac{7}{5}x+4$

Therefore, the equation of the line is $y=\dfrac{7}{5}x+4$. Hence, option A is correct.