Answer:
a) The equation of line perpendicular to above line and passes through point (-7,-4) is [tex]\mathbf{y=\frac{7}{2}x+\frac{41}{2}}[/tex]
b) The equation of line parallel to above line and passes through point (-7,-4) is [tex]\mathbf{y=-\frac{2}{7}x-6}[/tex]
Step-by-step explanation:
We are given the line: [tex]y=-\frac{2}{7}x-7[/tex]
The slope of the above equation is: [tex]m=-\frac{2}{7}[/tex] (By comparing with general form [tex]y=mx+b[/tex] where m is slope)
a) Find equation of line perpendicular to above line and passes through point (-7,-4)
If two lines are perpendicular there slopes are opposite reciprocal i.e [tex]m_1=-\frac{1}{m_2}[/tex]
The slope of new line will be: [tex]m = \frac{7}{2}[/tex]
Now finding y-intercept using slope and point (-7,-4)
[tex]y=mx+b\\-4=\frac{7}{2}(-7)+b \\-4=\frac{-49}{2}+b \\b=-4+\frac{49}{2}\\b=\frac{-8+49}{2}\\b=\frac{41}{2}[/tex]
So, the equation of line perpendicular to above line and passes through point (-7,-4) will be:
[tex]y=mx+b\\y=\frac{7}{2}x+\frac{41}{2}[/tex]
So, the equation of line perpendicular to above line and passes through point (-7,-4) is [tex]\mathbf{y=\frac{7}{2}x+\frac{41}{2}}[/tex]
b) Find equation of line parallel to above line and passes through point (-7,-4)
If two lines are parallel there slopes are same i.e [tex]m_1=m_2[/tex]
The slope of new line will be: [tex]m = -\frac{2}{7}[/tex]
Now finding y-intercept using slope and point (-7,-4)
[tex]y=mx+b\\-4=-\frac{2}{7}(-7)+b \\-4=-2(-1)+b\\-4=+2+b \\b=-4-2\\b=-6[/tex]
So, the equation of line parallel to above line and passes through point (-7,-4) will be:
[tex]y=mx+b\\y=-\frac{2}{7}x-6[/tex]
So, the equation of line parallel to above line and passes through point (-7,-4) is [tex]\mathbf{y=-\frac{2}{7}x-6}[/tex]
