Respuesta :
[tex]y = \frac{-1}{7}x -\frac{8}{7}[/tex] is the equation of the line that is perpendicular to this line and passes through the point (6, -2)
y = 7x - 44 equation of the line that is parallel to this line and passes through the point (6, -2)
Solution:
Given that line is:
y = 7x - 9
The equation of line in slope intercept form is given as:
y = mx + b ------ eqn 1
Where, "m" is the slope of line and "b" is the y intercept
On comparing eqn 1 with y = 7x - 9 we get,
m = 7
Find the equation of the line that is perpendicular to this line and passes through the point (6, -2)
We know that,
Product of slope of a line and slope of line perpendicular to given is always -1
Therefore,
[tex]7 \times \text{ slope of line perpendicular to it } = -1\\\\\text{ slope of line perpendicular to it } = \frac{-1}{7}[/tex]
Now find the equation of line:
[tex]\text{ Substitute } m = \frac{-1}{7} \text{ and } (x, y) = (6, -2) \text{ in eqn 1}[/tex]
[tex]-2 = \frac{-1}{7} \times 6 + b\\\\-2 = \frac{-6}{7} + b\\\\b = -2+\frac{6}{7}\\\\b = \frac{-14+6}{7}\\\\b = \frac{-8}{7}[/tex]
[tex]\text{Substitute } m = \frac{-1}{7} \text{ and } b = \frac{-8}{7} \text{ in eqn 1}\\\\y = \frac{-1}{7}x -\frac{8}{7}[/tex]
Thus the equation of line perpendicular to given line is found
Find the equation of the line that is parallel to this line and passes through the point (6, -2)
Slopes of parallel lines are equal
Therefore, m = 7
Substitute m = 7 and (x, y) = (6, -2) in eqn 1
-2 = 7(6) + b
-2 = 42 + b
b = -44
Substitute m = 7 and b = -44 in eqn 1
y = 7x - 44
Thus equation of line parallel to given line is found
