Equation of the Line Straight Lines Mr. J McCarthy.

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Presentation transcript:

Equation of the Line Straight Lines Mr. J McCarthy

xy

xy

xy

xy

xy Equation of the Line y=3

xy

xy

xy

xy

xy Equation of the Line x=2

xy 0 1 2

xy

xy

xy

xy Equation of the Line y = 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

xy

xy

xy

xy

xy Equation of the Line y = 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?  xY xY xY

Equation of the Line 

y = mx + c  y = x + 3 For 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 – 2 For 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) Rise Run

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 – y 1 = m(x – x 1 )  Example:  There is a line with a Point (4,2) and a slope of 3. What is the equation of the line?  y – y 1 = m(x – x 1 )  y – 2 = 3(x – 4)  y – 2 = 3x – 12  y = 3x –  y = 3x – 10 (x 1, y 1 ) 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 – y 1 = m(x – x 1 )  y – 2 = 3(x – 4)  y – 2 = 3x – 12  y = 3x –  y = 3x – 10 (x 1, y 1 )m

Junior Cert Question

Equation of the Line Question 1. The line K contains the point (2,4). K has a slope of 3. Find the equation of K. Answer: y – y 1 = m(x – x 1 ) y – 4 = 3(x – 2) y – 4 = 3x – 6 y = 3x – y = 3x – 2 y – y 1 = m(x – x 1 )<- Formula (x 1, y 1 ) m Question 2. The line K contains the point (4,5). K has a slope of 2. Find the equation of K. Answer: y – y 1 = m(x – x 1 ) y – 5 = 2(x – 4) y – 5 = 2x – 8 y = 2x – y = 2x – 3 (x 1, y 1 ) m Question 3. The line K contains the point (1,3). K has a slope of 5. Find the equation of K. Answer: y – y 1 = m(x – x 1 ) y – 3 = 5(x – 1) y – 3 = 5x – 5 y = 5x – y = 5x – 2 (x 1, y 1 ) m

Equation of the Line Question 4. The line K contains the point (3,1). K has a slope of 3. Find the equation of K. y – y 1 = m(x – x 1 )<- Formula Question 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 7. The line K contains the point (1,5). K has a slope of 2. 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. Question 9. The line K contains the point (4,3). K has a slope of 1. Find the equation of K.

Equation of the Line Question 4. The line K contains the point (3,1). K has a slope of 3. Find the equation of K. y – y 1 = m(x – x 1 )<- Formula Question 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.

Equation of the Line y – y 1 = m(x – x 1 )<- Formula Question 7. The line K contains the point (1,5). K has a slope of 2. 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. Question 9. The line K contains the point (4,3). K has a slope of 1. Find the equation of K.

Line Intersecting x and y axis Question 1. l is the line 2x + y = 4 L cuts the y-axis at the point T By Letting x = 0 find the co- ordinates of the point T. Answer: 2x + y = y = 4 y = 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  (x 1, y 1 )(x 2, y 2 ) (x 1, y 1 )(x 2, y 2 ) Steps  Formula  Labels  Replace  Simplify

Revision  (x 1, y 1 )(x 2, y 2 ) Steps  Formula  Labels  Replace  Simplify Equation of a Line Point (1,3) Slope = 5 y – y 1 = m(x – x 1 ) y – 3 = 5(x – 1) y – 3 = 5x – 5 y = 5x – y = 5x – 2 (x 1, y 1 ) m