Find the equation to the straight line which passes through the point

1.	Find the equation to the straight line which passes through the point (5, 6) and has intercepts on the axes(i) Equal in magnitude and both positive(ii) Equal in magnitude but opposite in sign
Answer» (i) Equal in magnitude and both positive Given: a = b Let us find the equation of line cutoff intercepts from the axes. By using the formula, The equation of the line is x/a + y/b = 1 x/a + y/a = 1 x + y = a The line passes through the point (5, 6) Hence, the equation satisfies the points. 5 + 6 = a a = 11 ∴ The equation of the line is x + y = 11 (ii) Equal in magnitude but opposite in sign Given: b = -a Let us find the equation of line cutoff intercepts from the axes. By using the formula, The equation of the line is x/a + y/b = 1 x/a + y/-a = 1 x – y = a The line passes through the point (5, 6) Hence, the equation satisfies the points. 5 – 6 = a a = -1 ∴ The equation of the line is x – y = -1

Find the equation to the straight line which passes through the point (5, 6) and has intercepts on the axes(i) Equal in magnitude and both positive(ii) Equal in magnitude but opposite in sign

Answer»

(i) Equal in magnitude and both positive

Given:

a = b

Let us find the equation of line cutoff intercepts from the axes.

By using the formula,
The equation of the line is x/a + y/b = 1

x/a + y/a = 1

x + y = a

The line passes through the point (5, 6)

Hence, the equation satisfies the points.

5 + 6 = a

a = 11

∴ The equation of the line is x + y = 11

(ii) Equal in magnitude but opposite in sign

Given:

b = -a

Let us find the equation of line cutoff intercepts from the axes.

By using the formula,
The equation of the line is x/a + y/b = 1

x/a + y/-a = 1

x – y = a

The line passes through the point (5, 6)

Hence, the equation satisfies the points.

5 – 6 = a

a = -1

∴ The equation of the line is x – y = -1