Straight Lines - Practice Questions & MCQ

Straight Line

It is a curve such that all points on the line segment joining any two points on it lies on it.

Every equation of first degree in x, y represents a straight line. General equation of a straight line is given as ax + by + c = 0 where a, b and c are real numbers and at least one of a and b is non-zero.

 

Slope of a Line

Slope of a line tells us the direction in which a line is drawn.

A line in a coordinate plane forms two angles with the x-axis, which are supplementary.

                 

The angle θ made by the line 'l' with the positive direction of the x-axis and measured anticlockwise is called the inclination of the line. θ lies in the range [0^o, 180^o)

If θ is the angle at which a straight line is inclined to a positive direction of the x-axis, then the slope (or gradient) of this line is defined by m = tan θ

Slope will be positive when θ is an acute angle and it will be negative when θ is an obtuse angle.

    

 

Note

• Slope is not defined for a vertical line, as θ = 90^o, and tan(90^o) is not defined.
• If a line is equally inclined with the coordinate axes then it will make an angle of 45^o and 135^o wrt positive direction of x-axis. In this case the slope will be tan(45^o) or tan(135^o). i.e. m = 1 or m = -1.

 

The slope of the line joining two given Points

If and are two points on a straight line then the slope of the line is 

.

 

Intercepts of a Line

X-Intercept: The x- coordinate of point where the straight line cuts x-axis.

Here straight line cuts X-axis at (x, 0) so

• x-intercept is x  (it can be positive or negative)
• Length of x-intercept is |x|.

y-intercept: The y- coordinate of point where the straight line cuts y-axis.

Here straight line cuts Y-axis at  (0, y) so

• y-intercept is y  (it can be positive or negative)
• Length of y-intercept is |y|.