Question

an equation of a line through (-4,-7) which is perpendicular to the line y = 5x +2

Answer 1

The sople of two perpendicular lines are opposite reciprocals. So if you have the slope of one line and need to know the slope of the line perpendicular to it you need to know that:

$m_1\cdot m_2=-1$

Where

m1: the slope of the first line

m2: the slope of the second line

In this case

m1= ?

m2=5

$m_1=-\frac{1}{m_2}=-\frac{1}{5}$The slope of the line perpendicular to y=5x+2 is -1/5

To determine the y intercept we have to find first the equation of the line:

$y=mx+b$

We have the m = -1/5

The b is calculated using the point (-4 , -7), as follow:

x=-4

y=-7

$y=mx+b$$-7=-\frac{1}{5}(-4)+b$$-7=\frac{1}{5}+b$$-7-\frac{1}{5}=b$$b=\frac{-35-1}{5}=-\frac{36}{5}$

The equation of the line is:

$y=-\frac{1}{5}x-\frac{36}{5}$

Knowing this we determine the y intercept when x=0:

$y=-\frac{1}{5}(0)-\frac{36}{5}$$y=-\frac{36}{5}$Then, the y intercept is : -36/5