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Straight Lines - Practice Questions & MCQ

Edited By admin | Updated on Sep 18, 2023 18:34 AM | #JEE Main

Quick Facts

  • Straight Line is considered one the most difficult concept.

  • 81 Questions around this concept.

Solve by difficulty

If \mathrm{x_{1}, x_{2}, x_{3}} as well as \mathrm{y_{1}, y_{2}, y_{3}} are in G.P., with the same common ratio, then the points \left(x_{1}\right.$, $\left.\mathrm{y}_{1}\right),\left(\mathrm{x}_{2}, \mathrm{y}_{2}\right)$ and $\left(\mathrm{x}_{3}, \mathrm{y}_{3}\right):

Concepts Covered - 1

Straight Line

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 [0o, 180o)

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

 

The slope of the line joining two given Points

If\mathrm{A\left ( x_1,y_1 \right )} and \mathrm{B\left ( x_2,y_2 \right )} are two points on a straight line then the slope of the line is 

.\tan\theta=\frac{BC}{AC}=\frac{y_2-y_1}{x_2-x_1}

 

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|.

 

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Straight Line

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