Equation of the Line Straight Lines Mr. J McCarthy

Equation of the LineStraight Lines

Mr. J McCarthy

x y

1

2

3

4

x y

1 3

2

3

4

x y

1 3

2 3

3

4

x y

1 3

2 3

3 3

4

x y

1 3

2 3

3 3

4 3

Equation of the Liney=3

x y

1

2

3

4

x y

2 1

2

3

4

x y

2 1

2 2

3

4

x y

2 1

2 2

2 3

4

x y

2 1

2 2

2 3

2 4

Equation of the Linex=2

x y

-1

0

1

2

x y

-1 -2

0

1

2

x y

-1 -2

0 -1

1

2

x y

-1 -2

0 -1

1 0

2

x y

-1 -2

0 -1

1 0

2 1

Equation of the Liney = x – 1

What is the relationship between x and y?

x is always 1 more than y.y is always 1 less than x.What is 1 less than x?

x – 1

x y

-3

0

1

2

x y

-3 0

0

1

2

x y

-3 0

0 3

1

2

x y

-3 0

0 3

1 4

2

x y

-3 0

0 3

1 4

2 5

Equation of the Liney = x + 3

What is the relationship between x and y?

x is always 3 less than y.y is always 3 more than x.What is 3 more than x?

x + 3

How to get the equation of a line when the line is on a Graph?

x Y

0 0

1 2

2 4

3 6

x Y

0 3

1 4

2 5

3 6

x Y

0 0

2 1

4 2

6 3

Equation of the Line

y = mx + c

y = x + 3For any line the

format of y = mx + c

m is the slope of the line

the point where it cuts the y axis is (0,c)

m = 1

(0,3)

y = mx + c

y = 2x – 2For any line the

format of y = mx + c

m is the slope of the line

the point where it cuts the y axis is (0,c)

m = 2

(0, – 2)

RiseRun

21

2

2

1

Equation of the Line formula

If we know a point on a line and the lines slope then we can use a formula to figure out the equation of the line:

y – y1 = m(x – x1) Example: There is a line with a Point (4,2) and a slope

of 3. What is the equation of the line? y – y1 = m(x – x1) y – 2 = 3(x – 4) y – 2 = 3x – 12 y = 3x – 12 + 2 y = 3x – 10

(x1,y1) m

Equation of the Line formula

There is a line with a Point (4,2) and a slope of 3. What is the equation of the line?

y – y1 = m(x – x1) y – 2 = 3(x – 4) y – 2 = 3x – 12 y = 3x – 12 + 2 y = 3x – 10

(x1,y1) m

Junior Cert Question


Question 1.The line K contains the point (2,4).K has a slope of 3.Find the equation of K.Answer:y – y1 = m(x – x1)

y – 4 = 3(x – 2)y – 4 = 3x – 6y = 3x – 6 + 4y = 3x – 2

y – y1 = m(x – x1)

<- Formula

(x1,y1)

m


y – 5 = 2(x – 4)y – 5 = 2x – 8y = 2x – 8 + 5y = 2x – 3

(x1,y1)

m


y – 3 = 5(x – 1)y – 3 = 5x – 5y = 5x – 5 + 3y = 5x – 2

(x1,y1)

m


Question 4.The line K contains the point (3,1).K has a slope of 3.Find the equation of K.

y – y1 = m(x – x1)

<- FormulaQuestion 5.The line K contains the point (4,2).K has a slope of 2.Find the equation of K.

Question 6.The line K contains the point (-3,2).K has a slope of 4.Find the equation of K.


Question 8.The line K contains the point (3,-2).K has a slope of 5.Find the equation of K.




y – y1 = m(x – x1)


Question 6.The line K contains the point (-3,2).K has a slope of 4.Find the equation of K.

Equation of the Liney – y1 = m(x – x1)


Question 8.The line K contains the point (3,-2).K has a slope of 5.Find the equation of K.


Line Intersecting x and y axis

Question 1.l is the line 2x + y = 4L cuts the y-axis at the point TBy Letting x = 0 find the co-ordinates of the point T.Answer:2x + y = 40 + y = 4y = 4

(The line l cuts the y axis at the point (0,4) )

Find Co-Ordinates of the points where these lines cut the x and y axis

Revision

(x1,y1) (x2,y2) (x1,y1) (x2,y2)

StepsFormulaLabelsReplaceSimplify

Revision

(x1,y1) (x2,y2)

StepsFormulaLabelsReplaceSimplify

Equation of a Line

Point (1,3)

Slope = 5

y – y1 = m(x – x1)

y – 3 = 5(x – 1)

y – 3 = 5x – 5

y = 5x – 5 + 3

y = 5x – 2

(x1,y1)

m

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Equation of the Line Straight Lines Mr. J McCarthy