Which of these lines have a positive gradient B C D Which of these lines have a positive gradient

Which line has the largest positive gradient? B C D Which line has the largest positive gradient?

Which of these lines have a negative gradient? B C D Which of these lines have a negative gradient?

Which of these lines has a negative gradient closest to 0 ? B C D Which of these lines has a negative gradient closest to 0 ?

Which of these lines has the largest y-intercept? B C D Which of these lines has the largest y-intercept?

Which of these lines has the smallest y-intercept? B C D Which of these lines has the smallest y-intercept?

Parallel Lines Remember from a previous lesson: The general equation of a straight line can be written as:       This is called the y-intercept and it has the coordinate (0, c). For example, the line y = 3x + 4 has a gradient of 3 and crosses the y-axis at the point (0, 4).

Write the gradient of the following lines In your books: Write the gradient of the following lines Equation Gradient y = 2x + 1 m = 2 y = 2 + 4x m = 4 y = 3x + 2 m = 3 y + 2x = 2 m = -2 What were the common mistakes? What must you remember to do when finding the gradient from an equation? Challenge: 2y = 3x – 2 5y + 2x = 3

What do you know about the gradients of parallel lines? Remember: What do you know about the gradients of parallel lines? We have seen that parallel lines have gradients that are equal

Are these lines parallel? They look parallel, but how can we be certain? We can compare their gradients

Write an equation of a line that is parallel to these In your books: Write an equation of a line that is parallel to these Equation Gradient A Parallel Line y = 2x + 1 m = 2 y = 2x + c y = 2 + 4x m = 4 y = 4x + c y = 3x + 2 m = 3 y = 3x + c y + 2x = 2 m = -2 y = -2x + c Challenge: 2y = 3x – 2 5y + 2x = 3

Consider the following line that has a gradient of 2: y y1 x On your whiteboards: Show me an equation of a line that would be parallel to this line and another …

Consider the following line that has a gradient of 2: y y1 x Discuss: How many lines are there that are parallel to this one?

Consider the following line that has a gradient of 2: y y1 x Discuss: How could I change my question so there was only one possible equation as an answer? What other information would you need?

To do this we must also have a coordinate on the new line. There are an infinite number of lines that are parallel to the one I have drawn … We do not have enough information to determine which particular line it is. ? y ? y1 ? x To do this we must also have a coordinate on the new line.

What information do you know about the new line? Find the equation of the line that is parallel to y = 3x + 2 and that passes through the point (0, -1) Discuss: What information do you know about the new line?

Find the equation of the line that is parallel to y = 3x + 2 and that passes through the point (0, -1) How can we find the gradient of the new line? What will the y-intercept of the new line be? What is the equation of the new line?

On your whiteboards… Find the equation of the line that is parallel to y = 2x + 5 and that passes through the point (0, 1) m = c = Print this slide for students to attempt Equation

Find the equation of the line parallel to y = 5x - 4 that passes through (3, 16)  

Find the equation of the line parallel to y = 5x - 4 that passes through (3, 16) We don’t know the y-intercept and so must find it. The line is parallel, so we need an equal gradient. We don’t know c at this stage y = 5x + 1 y = 5x + ? y y = 5x - 4 1 x   -4 Simplify by doing the calculation   So what is c?    

Spot the mistakes: y = 2x + c 9 = 2(3) + c 9 = 5 + c 14 = c Find the equation of the line which is parallel to y = 2x + 3 and passes through the point (9, 3). y = 2x + c 9 = 2(3) + c 9 = 5 + c 14 = c y = 2x + 14

Spot the mistakes: y = 2x + c 9 = 2(3) + c 9 = 5 + c 14 = c Find the equation of the line which is parallel to y = 2x + 3 and passes through the point (9, 3). y = 2x + c 9 = 2(3) + c 9 = 5 + c 14 = c y = 2x + 14

On your whiteboards… Find the equation of the line that is parallel to the line y = 2x + 15 that passes through the point (2 , 10) y = 2x + 6

On your whiteboards… Find the equation of the line that is parallel to the line y = 4x - 22 that passes through the point (3 , 14) y = 4x + 2

In your books Find the equations for the straight lines described below.   1) Parallel to y = 3x – 18 and goes through (3,2). 2) Parallel to y = 5x + 10 and goes through (4, 10). 3) Parallel to y = 2x + 5 and goes through (1, 18). 4) Parallel to y = 4 - 2x and goes through (3, 1). 5) Parallel to y = -3x + 5 and goes through (-6, 3). Only use if need more practice

Answers y = 3x – 7 2) y = 5x – 10 3) y = 2x + 16 4) y = -2x + 7