Straight Lines Objectives E Grade Plot the graphs

Straight Lines Objectives: E Grade Plot the graphs of straight lines such as x = 3 and y = 4 Complete a table of values for equations such as y = 3 x + 1 and draw the graph D Grade Solve problems involving graphs, such as finding where the line y = x +3 crosses the line y = 2 C Grade Recognise the equations of straight line graphs such as y = -3 x + 1 Find the gradients of straight line graphs Prior knowledge: Plot co-ordinates in all four quadrants

Straight Lines In order to plot straight lines we must be able to substitute numbers into an equation in order to calculate a value. Try these: Using the value given for x, calculate the value for y y = x + 2 for x = 2 y = x + 10 for x = 3 y = 4 y = 13 y = x + 3 for x = -6 y = x – 2 for x = 3 y = -3 y = 1 -3 for x = -3 y = -6 y = x y = 2 x - 5 for x = 5 y = 5 y = -3 x -5 for x = 2. 5 y = -6 x + 5 for x = -3. 5 y = -12. 5 y = 26

Straight Lines When given an equation and told to plot a graph, first find coordinates of points on the line, this is done by completing a table. By substituting the given values for x calculate the y value for the following equation: y = x + 2 x -3 -2 -1 0 1 2 3 y -1 0 1 3 5 2 4 This generates coordinates to plot on a graph (-3, -1) (-2, 0) (-1, 1) (0, 2) (1, 3) (2, 4) (3, 5)

Plotting these points (-3, -1) (-2, 0) (-1, 1) (0, 2) Straight Lines (0, 2) (1, 3) (2, 4) (3, 5) y 10 9 8 7 6 5 4 3 x x x 2 We find a straight line-10 x 1 -9 -8 -7 -6 -5 -4 -3 x x -1 -2 0 -1 -2 -3 -4 -5 -6 -7 -8 -9 -10 1 2 3 4 5 6 7 8 9 10 x

Straight Lines Copy and complete this table for the following equation and plot the y straight line 10 9 y = 3 x - 1 x 8 7 6 x y -3 -1 -10 -4 0 -1 1 2 3 8 5 4 3 2 x 1 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 x -1 -2 -3 x -4 -5 -6 -7 -8 x -9 -10 1 2 3 4 5 6 7 8 9 10 x

Complete the table for the equation y = x x -3 -1 0 1 1 y - 3 - 1 0 Complete the table for the equation y = x +1 x -3 -1 0 1 - 2 0 1 y 2 Complete the table for the equation y = x + 3 x -3 -1 0 1 2 3 0 4 y Complete the table for the equation y = x - 2 x -3 -1 0 1 y -5 -3 -2 -1 Straight Lines 3 3 Plot the coordinates When the table is completed y 10 9 8 7 3 4 3 6 5 4 x 3 -10 -9 -8 -7 -6 -5 -4 x x 2 x x 1 x x x xx 1 2 3 4 -3 -2 -1 0 x -1 x x -2 x x x -3 x -4 -5 -6 3 1 x 6 -7 -8 -9 -10 5 6 7 8 9 10 x

Straight Lines What do you notice about these straight lines? y=x+1 y=x+3 y=x-2 They are parallel to each other i. e. they have the same -10 gradient The number added to x is where the line crosses the y axis y 10 9 8 7 x 6 5 4 x 3 -9 -8 -7 -6 -5 -4 x x 2 x x 1 x x x xx 1 2 3 4 -3 -2 -1 0 x -1 x x -2 x x x -3 x -4 -5 -6 -7 -8 -9 -10 5 6 7 8 9 10 x

Straight Lines We start with the line y = x y To become y = x + 1 The line moves up by 1 and crosses the y axis at 1 10 9 8 7 6 5 4 Start again with the line y = x To become y = x + 4 The line moves up by 4 and crosses the y axis at 4 -10 -9 3 2 1 -8 -7 -6 -5 -4 -3 -2 -1 0 -1 -2 -3 -4 -5 -6 -7 -8 -9 -10 1 2 3 4 5 6 7 8 9 10 x

Straight Lines Write the equations of these lines? 1 2 3 4 5 1 y 10 y = x + 6 y = x + 2 y = x - 1 y = x - 5 y = x - 9 2 9 8 7 3 6 5 4 4 3 2 5 1 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 -1 -2 -3 -4 -5 -6 -7 -8 -9 -10 1 2 3 4 5 6 7 8 9 10 x

Straight Lines To summarise for where a line crosses the y-axis Known as the y intercept For any equation in the form y = x + c The variable c can be + or c is where the line crosses the y axis

Straight Lines y 10 9 8 7 6 5 4 3 2 1 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 -1 -2 -3 -4 -5 -6 -7 -8 -9 -10 1 2 3 4 5 6 7 8 9 10 x

Complete the table for the equation y = x x -3 -1 0 1 y Complete the table for the equation y = x +1 x -3 -1 0 1 y Complete the table for the equation y = x + 3 x -3 -1 0 1 y Complete the table for the equation y = x - 2 x -3 -1 0 1 y Worksheet 1 Straight Lines Plot the coordinates When the table is completed y 3 10 9 8 7 6 3 5 4 3 2 1 3 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 -1 -2 -3 -4 -5 -6 3 -7 -8 -9 -10 1 2 3 4 5 6 7 8 9 10 x

Worksheet 2 Straight Lines Write the equations of these lines? 1 y 10 1 2 3 4 5 2 9 8 7 3 6 5 4 4 3 2 5 1 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 -1 -2 -3 -4 -5 -6 -7 -8 -9 -10 1 2 3 4 5 6 7 8 9 10 x