Question

find the equation of the straight line passing through the origin and making equal angels with coordinate axes​

Answer 1

$\huge{\boxed{\red{\star\;Answer}}}$

$\large{\underline{\pink{\star\;Note}}}$

• If the line makes equal angles with coordinate axes then the angle made by the x-axis would be 45° or 135°
• Hence there would be two possible values for the slope.
• The values of slopes are m1 = 1 and m2 = -1

• When a point on the line (a,b) and slope is given the line equation is
• y-b = m(x-a)

Here the values are

• Given line passes through origin , hence
• a = 0 and b = 0
• Also slopes of line are m1 = 1 and m2 = -1

$\large{\underline{\blue{Equation\;of\;line\;1}}}$

• a = 0 and b = 0 m1 = 1
• Equation is y-b = m(x-a)
• y-0 = 1(x-0)
• y = x
• x - y = 0

$\large{\boxed{\green{Equation\;of\;1st\;line\;is\;x-y=0}}}$

$\large{\underline{\blue{Equation\;of\;line\;}}}$

• a = 0 and b = 0 m2 = -1
• Equation is y-b = m(x-a)
• y-0 = -1(x-0)
• y = -x
• x + y = 0

$\large{\boxed{\green{Equation\;of\;2nd\;line\;is\;x+y=0}}}$

$\large{\boxed{\red{The\;equations\;required\;are\;x-y=0\;and\;x+y=0}}}$