Problems on Slope and Intercept

We will learn how to solve different type of problems on slope and intercept from the given equation.

1. Find the slope and y-intercept of the straight-line 5x - 3y + 15 = 0. Find also the length of the portion of the straight line intercepted between the co-ordinate axes.

Solution:  

The equation of the given straight line is,

5x - 3y + 15 = 0           

⇒ 3y = 5x + 15                

⇒ y = 53x + 5 

Now, comparing equation y = 53x + 5 with the equation y = mx + c we get,

m = 53 and c = 5.

Therefore, the slope of the given straight line is 53 and its y-intercept = 5 units.

Again the intercept form of the equation of the given straight line is,

5x - 3y + 15 = 0

⇒ 5x - 3y = -15

5x15 - 3y15 = 1515

x3 + y5 = 1

Clearly, the given line intersects the x-axis at A (-3, 0) and the y-axis at B (0, 5).

Therefore, the required length of the portion of the line intercepted between the co-ordinates axes

= AB

= (3)2+52

= 9+25 units.

= √34 units.

2. Find the equation of the straight line passes through the point (2, 3) so that the line segment intercepted between the axes is bisected at this point.

Solution:

Let the equation of the straight line be xa + yb = 1, which meets the x and y axes at A (a, 0) and B (0, b) respectively. The coordinates of the mid-point of AB are (a2, b2). Since the point (2, 3) bisects AB, therefore

a2 = 2 and b2 = 3

⇒ a = 4 and b = 6.

Therefore, the equation of the required straight line is x4 + y6 = 1 or 3x + 2y = 12.


More examples to solve the problems on slope and intercept.

3. Find the equation of the straight line passing through the points (- 3, 4) and (5, - 2); find also the co-ordinates of the points where the line cuts the co-ordinate axes.

Solution:   

The equation of the straight line passing through the points (- 3, 4) and (5, - 2) is

y4x+3 = 4+235, [Using the form, y - y1 = y2y1x2x1 (x - x1)]

y4x+3 = 68

y4x+3 = 34

⇒ 3x + 9 = - 4y + 16

⇒ 3x + 4y = 7 ………………… (i)

3x7 + 4y7 = 1        

x73 + y74 = 1

Therefore, the straight line (i) cuts the x-axis at (73, 0) and the y-axis at (0, 74).

 The Straight Line





11 and 12 Grade Math 

From Problems on Slope and Intercept to HOME PAGE




Didn't find what you were looking for? Or want to know more information about Math Only Math. Use this Google Search to find what you need.



New! Comments

Have your say about what you just read! Leave me a comment in the box below. Ask a Question or Answer a Question.




Share this page: What’s this?

Recent Articles

  1. Quadrilaterals | Four Sided Polygon | Closed Figure | Adjoining Figure

    Jul 14, 25 02:55 AM

    Square
    Quadrilaterals are known as four sided polygon.What is a quadrilateral? A closed figure made of our line segments is called a quadrilateral. For example:

    Read More

  2. Formation of Numbers | Smallest and Greatest Number| Number Formation

    Jul 14, 25 01:53 AM

    In formation of numbers we will learn the numbers having different numbers of digits. We know that: (i) Greatest number of one digit = 9,

    Read More

  3. 5th Grade Geometry Practice Test | Angle | Triangle | Circle |Free Ans

    Jul 14, 25 01:53 AM

    Name the Angles
    In 5th grade geometry practice test you will get different types of practice questions on lines, types of angle, triangles, properties of triangles, classification of triangles, construction of triang…

    Read More

  4. 5th Grade Circle Worksheet | Free Worksheet with Answer |Practice Math

    Jul 11, 25 02:14 PM

    Radii of the circRadii, Chords, Diameters, Semi-circles
    In 5th Grade Circle Worksheet you will get different types of questions on parts of a circle, relation between radius and diameter, interior of a circle, exterior of a circle and construction of circl…

    Read More

  5. Construction of a Circle | Working Rules | Step-by-step Explanation |

    Jul 09, 25 01:29 AM

    Parts of a Circle
    Construction of a Circle when the length of its Radius is given. Working Rules | Step I: Open the compass such that its pointer be put on initial point (i.e. O) of ruler / scale and the pencil-end be…

    Read More