1 / 13

Mastering Straight Line Graphs: Plotting, Solving & Recognizing Equations

Learn to plot, solve problems, and recognize equations of straight lines. Complete tables, draw graphs, and find where lines cross. Dive into graphing equations like y=x+3 and y=-3x+1. Prior knowledge of plotting coordinates needed.

zacharyo
Download Presentation

Mastering Straight Line Graphs: Plotting, Solving & Recognizing Equations

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. 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 = 3x + 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 = -3x + 1 Find the gradients of straight line graphs Prior knowledge: Plot co-ordinates in all four quadrants

  2. 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 = x + 3 for x = -6 y = x – 2 for x = 3 y = x -3 for x = -3 y = 2x - 5 for x = 5 y = -3x -5 for x = 2.5 y = -6x + 5 for x = -3.5 Straight Lines In order to plot straight lines we must be able to substitute numbers into an equation in order to calculate a value. y = 4 y = 13 y = -3 y = 1 y = -6 y = 5 y = -12.5 y = 26

  3. 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 -1 0 1 3 5 2 4 This generates coordinates to plot on a graph (-3,-1) (0, 2) (1, 3) (-2,0) (-1, 1) (2, 4) (0, 2) (3, 5)

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

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

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

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

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

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

  10. 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

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

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

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

More Related