Question 1: Reduce the equation to:

(i) slope-intercept form and find slope and y-intercept (ii) intercept form and find intercept on the axes; (iii) the normal form and find .

Answer:

i)

ii)

iii)

Since the coefficient of both are negative, lies in the Quadrant.

Question 2: Reduce the following equations to the normal form and find in each case:

i) ii) iii)

iv) v)

Answer:

i)

Since the coefficient of both are positive, lies in the Quadrant.

ii)

Since the coefficient of both are negative, lies in the Quadrant.

iii)

Since the coefficient of both is negative and y is positive, lies in the Quadrant.

iv)

v)

Question 3: Put the equation to the slope intercept form and find its slope and y-intercept.

Answer:

Comparing with

Question 4: Reduce the lines to the normal form and hence find which line is nearer to the origin.

Answer:

Since , we can say that is nearer to the origin as compared to

Question 5: Show that the origin is equidistant from the lines ; .

Answer:

Since , the given lines ; are equidistance from the origin.

Question 6: Find the values of , if the equation is the normal form of the line .

Answer:

Question 7: Reduce the equation to the intercept form and find the intercepts.

Answer:

Question 8: The perpendicular distance of a line from the origin is units and its slope is . Find the equation of the line.

Answer:

Therefore equation of line:

Comparing with

Slope

Therefore the equation of line is