Module :MA0001NPFoundation Mathematics

Lecture Week 7

THE STRAIGHT LINE

DISTANCE AND GRADIENTS • The distance between two points P(x1,y1) and

Q(x2,y2) is Distance PQ =

• The slope or gradient of the line joining two Points P(x1,y1) and Q(x2,y2) is Slope (m) = y2-y1/x2-x1

2122

12 yyxx

Equation of straight lines Slope intercept form : The equation of the form Y = mx + c is called slope intercept form of the

straight line .Where ,m = slope of the line C= y – intercepts For eg : y = 2x +3

O

y

x

O

y

x

c

A(0, c)

xP(x, y)

Slope = m

Slope-Intercept Form

Given a straight line which cuts the y-axis at A and with slope m .

(Note: c is called the y-intercept of the straight line.)

If P is any point on the line, then

Slope of PA = 0

x

cy

Equation of straight lines Two point form or Double point form : The equation of the straight line passing

through two points P(x1,y1) and Q(x2,y2) is

y-y1=m(x-x1)Where, m = slope= y2-y1/x2-x1

x 22 , yxBy

Ox

x

11, yxA

x yxP ,

Two-Point Form

Given a straight line which passes through the points A and B, then

12

12

xx

yy

Slope of AB(m)=

If P(x, y) is any point on the line AB, then

1

1

xx

yy

Slope of

PA(m) =

Equation of straight lines Double intercepts form : The equation of the form,

x/a + y/b = 1 is called the equation of the straight line in

double intercepts form .

Double Intercept Form

x

xa

b

Given a straight line which cuts the x-axis at A and y-axis at B.

(Note: a is called the x-intercept of the straight line.)

x

y

Ox

B(0, b)

A(a, 0)

P(x, y)

=

a

b

0

0Slope of AB =

a

b

ax

y

0

Slope of PA =

If P is any point on the line, then

General Form of a straight line

It should be noted that all the different standard forms of the equation of a straight line can be reduced to the form

Ax + By + C = 0

where A, B and C are constants with A and B not both zero.

This equation is known as the General Form of a straight line.

Q1. Find the distance between the following pair of points. Also find the slope of the line joining these points.a . (0 , 0) and (3 , 4)b . ( 2 , 3) and (6 , 4)c . (-2 , 3) and (2 , 0)d . (a , 0) and (0 , b)

Exercises…

Q2.If the line joining (2, y) and (4, 6) has slope -3/2, find the distance between them.

Exercises…

Q3.Find the value of y when the distance between the points (3, y) and (4, 1) is √10.Also find the slope of the line joining the two points.

Q4.The distance between A (1, 3) and B(x,7) is 5. Calculate the possible values of x and the slope of AB.

Exercises…

Q5.Find the equation of the straight line with y- intercept 3 and parallel to the straight line 2x - y = - 3.

Q6.The equation of a straight line is 3y + 2x +6 = 0. Calculatea. The gradientb. The coordinates of the point where it cuts x-axisc. The coordinates of the point where it cuts the line

y=4d. The equation of the line parallel to it and passing

through (5,2)

Exercises…