Slope-intercept Form of a Straight Line

We will discuss here about the method of finding the equation of a straight line in the slope-intercept form.

Let the straight line AB intersect x-axis at C and y-intersect at D.

Let ∠ACX = θ and OD = c.

Then, tan θ = m(say).

We have to find the equation of the straight line AB.

Now take any point P (x, y) on the line. Let PM  ⊥ OX.

Then, OM = x and PM = y.

Draw DE ⊥ PM. Clearly, DE ∥ OX.

Also, PE = PM – EM = PM - OD = y - c, and DE = OM = x.

As DE ∥ OX, ∠PDE = ∠PCX = θ. Therefore, in the right-angled triangle PED,

tan θ = \(\frac{PE}{DE}\) = \(\frac{y - c}{x}\)

⟹ m = \(\frac{y - c}{x}\)

⟹ y – c = mx

⟹ y = mx + c

This is the relation between the x-coordinate and y-coordinate of any point on the line AB.

y = mx + c is the equation of the straight line whose slope is m and which cuts off an intercept c on the y-axis.


Solved examples of finding the equation of a straight line in the slope-intercept form:

1. The equation of the straight line inclined at 30° with the positive direction of the x-axis and cuts an intercept 5 units on the positive direction of the y-axis is

y = tan 30° ∙ x + 5, (since m = tan 30° and c = +5)

⟹ y = \(\frac{√3}{3}\)x + 5


2. The equation of the straight line inclined at 45° with the positive direction of the x-axis and cuts an intercept 7 units on the positive direction of the y-axis is

y = tan 45° ∙ x + (-7), (since m = tan 45° and c = -7)

⟹ y = x – 7


Notes:

I. The x-axis is inclined at 0° with the positive direction of the x-axis i.e. m = tan 0and cuts at intercept 0 unit on the y-axis i.e. c = 0. So, the equation of the x-axis is y = tan 0° ∙ x + 0, (since m = tan 0° and c = 0)

⟹ y = x + 0 or x

Therefore, the equation of the x-axis is y = 0


II. If a line parallel to x-axis and at a distance a from the x-axis then the slope m = tan 0 and the intercept on the y-axis c = a. So, the equation of the parallel line is y = tan 0 ∙ x + a, (since m = tan 0° and c = a)






10th Grade Math

From Slope-intercept Form of a Straight Line to HOME




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. Formation of Square and Rectangle | Construction of Square & Rectangle

    Jul 16, 25 02:45 AM

    Construction of a Square
    In formation of square and rectangle we will learn how to construct square and rectangle. Construction of a Square: We follow the method given below. Step I: We draw a line segment AB of the required…

    Read More

  2. Perimeter of a Figure | Perimeter of a Simple Closed Figure | Examples

    Jul 16, 25 02:33 AM

    Perimeter of a Figure
    Perimeter of a figure is explained here. Perimeter is the total length of the boundary of a closed figure. The perimeter of a simple closed figure is the sum of the measures of line-segments which hav…

    Read More

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

    Jul 15, 25 11:46 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

  4. 5th Grade Quadrilaterals | Square | Rectangle | Parallelogram |Rhombus

    Jul 15, 25 02:01 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

  5. 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