Equation of a Straight Line

You will probably recognise the most commonly used form of the equation of a straight line: y = mx + c where m represents the gradient and c represents the y-intercept. It is important not to overlook this topic, as it comes up a lot in work on Functions, Vectors and Calculus. Make sure that you can use all three forms of the equation of a straight line, as this will help you with the Equation of Tangent and Normal.


 

 

Key Concepts

On this page, you should learn to

  • Use the three different forms of the equations of straight lines
    • \(y = mx + c \)
    • \(ax+by + d = 0 \)
    • \(y-y_1=m(x-x_1) \)
  • Solve problems with parallel lines \(m_1=m_2\)
  • Solve problems with perpendicular lines \(m_1 \times m_2=-1\)

Summary

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Test Yourself

Here is a quiz that practises the skills from this page


START QUIZ!

Here is a quiz about parallel and perpendicular lines


START QUIZ!

Exam-style Questions

Question 1

The line \(l_1\) has equation 2x+5y+6=0

The line \(l_2\) is perpendicular to the line \(l_1\)and passes through the point (2 , -2)

a) Find the equation of \(l_2\)in the form ax+by+d=0, where a, b and d are constants.

b) Find the coordinates where \(l_2\) meets the y axis


Hint

Full Solution

Question 2

The point A has coordinates (a , 3) and the point B has coordinates (7 , b).

The line AB has equation 2x + 3y = 11.

a) Find the values of a and b

The line AC is perpendicular to the line AB.

b) Find the equation of the line AC in the form ax + by + d = 0, where a, b and d are constants

c) Given that C lies on the x axis, find its coordinates.

Hint

Full Solution

 

 Question 3

The line \(l_1 \) passes through the point P(3k , 2k) with gradient = -2.

\(l_1 \) meets the x axis at A and the y axis at B.

a) Find the equation of the line \(l_1 \) and show that A(4k , 0)

b) Find the area of the triangle AOB in terms of k

The line \(l_2\) passes through P and is perpendicular to \(l_1 \)

c) Find the equation of \(l_2\)

\(l_2\)meets the x axis at C

d) Show that the midpoint of PC lies on the line y = x


Hint

Full Solution

 

Question 4

Point A has coordinates (a , 6) and point B has coordinates (5 , b).

The line 8x - 6y + 3 = 0 is the perpendicular bisector of AB.

Find a and b.

Hint

Full Solution

 

MY PROGRESS

How much of Equation of a Straight Line have you understood?