Straight Line Graphs Int 2 Drawing Straight line

Straight Line Graphs Int 2 Drawing Straight line graphs The gradient from coordinates The y intercept y = ax + b Other forms / rearranging equation 15 -Mar-18

Starter Questions Int 2 Q 1. A house is valued at £ 50 000. Calculate it’s value after 4 years if it appreciates by 5% each year. Q 2. Calculate 3. 36 x 70 to 2 significant figures. Q 3. Calculate the volume of a cylinder with radius 5 cm and height 100 cm. 15 -Mar-18

Straight Line Graphs Int 2 Learning Intention 1. To draw graphs by using a coordinate table Success Criteria 1. Understand the keypoints of drawing a straight line graph 2. Be able to plot a straight line graph 15 -Mar-18

Drawing Straight Line Graphs y = ax + b y y=x 10 y = 3 x+1 x 8 x -2 0 2 7 0 3 -4 y 9 0 3 -4 6 y -5 1 7 5 4 3 2 1 -10 -9 y=x-3 x 0 4 8 y -3 1 5 -8 -7 -6 -5 -4 -3 -2 -1 0 -1 -2 -3 -4 -5 -6 -7 -8 -9 -10 15 -Mar-18 1 2 3 4 5 6 7 8 9 10 x y = 2 x x 0 3 -4 y 6 -8 0

Straight Line Graphs Int 2 Key Points 1. Make a table 2. Calculate and plot 3 coordinates 3. Draw a line through points 15 -Mar-18

Straight Line Graphs Int 2 Now try Exercise 1 Odd numbers MIA (page 33) 15 -Mar-18

Starter Questions Int 2 Q 1. Write this number in full to 1 sig. figs Q 2. Calculate the volume of the triangular prism. 20 cm 12 cm 8 cm 15 -Mar-18

The Gradient of a Line Int 2 Learning Intention 1. To explain how to calculate the gradient using right angle triangles Success Criteria 1. Gradient is : change in vertical height divided by change in horizontal distance 2. Calculate simple gradients. 15 -Mar-18

The Gradient Difference in Int 2 y -coordinates The gradient is the measure of steepness of a line Change in vertical height Change in horizontal distance Difference The steeper a line the bigger the gradient in x -coordinates 15 -Mar-18

The Gradient Int 2 3 4 3 2 3 5 2 15 -Mar-18 6

The Gradient Int 2 Round the class Exercise 2 MIA (page 36) 15 -Mar-18

The Gradient of a Line Int 2 Learning Intention 1. To explain positive and negative gradients using coordinates. 15 -Mar-18 Success Criteria 1. Know gradient formula. 2. Calculate gradients given two coordinates.

The gradient using coordinates Int 2 a = gradient y-axis y 2 y 1 O 15 -Mar-18 x 1 x-axis x 2 13

The gradient using coordinates Int 2 Find the gradient of the line. y-axis O 15 -Mar-18 a = gradient x-axis 14

The gradient using coordinates Int 2 Find the gradient of the two lines. y-axis O 15 -Mar-18 x-axis 15

The gradient using coordinates Int 2 The gradient formula is : It is a measure of how steep a line is A line sloping up from left to right is a positive gradient A line sloping down from left to right is a negative gradient 15 -Mar-18

The gradient using coordinates Int 2 Exercise 3 Q 1 – Q 3 MIA (page 37) 15 -Mar-18

Starter Questions Int 2 Q 1. Write out in full to 2 sig. figs. Q 2. A superstore make 20% profit on each can of soup they sell. If they buy in a can for 50 p. What is the selling price. Q 3. A hemisphere has a diameter of 10 cm. Calculate its volume. 15 -Mar-18

The Gradient of a Line Int 2 Learning Intention 1. To explain the connection between the straight line equation and the gradient. 15 -Mar-18 Success Criteria 1. Understand the term standard form. 2. Identity the gradient a from the standard form.

Straight line equation and the gradient connection y 10 y = 2 x - 5 x 9 y = 2 x + 1 8 1 3 7 y -5 -3 1 5 0 x 0 4 1 3 y 6 3 7 1 3 2 1 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10 x -1 -2 -3 -4 -5 a=2 -6 -7 -8 -9 -10 15 -Mar-18 a=2

Straight Line Equation y All straight lines have the equation of the form lines are parallel if they have the same gradient Where line Gradient meets y-axis y = ax + b 10 9 8 7 6 5 4 3 2 1 0 1 2 3 4 5 6 7 8 9 10 x Find the equations of the following lines y = x 15 -Mar-18 y = x+4 y = 4 x+2 y = -0. 5 x+2

The Gradient of a Line Int 2 Now try Exercise 3 Q 4 – Q 9 MIA (page 38) 15 -Mar-18

Starter Questions Int 2 Q 1. Write out in full to 1 significant fig. Q 2. A computer store buys in a laptop for £ 500. They want to make a 40% profit. How much do they sell it for. Q 3. A line is parallel to y = 2 x. Write down its equation 15 -Mar-18

lines are parallel if. Straight same gradient Line Equation All straight lines have the equation of the form y = ax + b Slope left to right upwards positive gradient Gradient Slope left to right downwards negative 15 -Mar-18 gradient y - intercept y intercept is were line cuts y axis

Straight Line Graphs Int 2 Now try Exercise 4 MIA (page 41 ) 15 -Mar-18

Starter Questions Int 2 Q 1. The points ( 1, 4) and (3, 11) lie on a line. Find the gradient of the line. Q 2. Complete the table given : x y Q 3. -3 0 3 Are the two lines parallel. Explain answer y=x+2 15 -Mar-18 y = 3 x+1 and y = 2 x + 2

Straight Line Equation Int 2 Learning Intention Success Criteria 1. To show to rearrange straight line equations into standard form and then identify the gradient and the y - intercept. 1. Be able to rearrange straight line equations. y = ax + b 2. Identify the gradient a and y – intercept b from the standard form. y = ax + b 15 -Mar-18

Straight Line Equation This called All straight lines have an equation of the form the standard form y = ax + b Gradient Where line meets y-axis If two lines have the same gradient they are parallel. y = 2 x 15 -Mar-18 y = 2 x+4

Just a bit of Straight algebra Line Equation Rearrange the following straight line equations into standard form and identify the gradient and y-intercept. Standard form a b y = 3 x + 4 3 4 2 y – 2 x = 6 y =x+3 1 3 y–x+5=0 y=x-5 1 -5 y=2 0 2 y – 3 x = 4 4 y – 8 = 0 15 -Mar-18

Straight Line Equation Find the a line parallel to y – x = 0 and passing through (0, 3). Standard form x–y=0 a 1 y =x b 0 A line parallel to y = x has same gradient therefore a = 1 Since it passes through (0, 3) then b = 3 Using standard form line is 15 -Mar-18 y=x+3

Straight Line Equation Int 2 Now try Ex 5 MIA (page 45) 15 -Mar-18