Created by Mr Lafferty BscHons Math SciOpen GIMA
Created by Mr. Lafferty Bsc(Hons) Math. Sci(Open) GIMA www. mathsrevision. com Higher Still Course m>0 m<0 m=0 y=c Presentation on Straight Line Theory Click button to begin y = mx+c x=a 9/25/2020 www. mathsrevision. com 1
Essential Information y = mx+c § Standard form for a Straight Line m>0 § What you need to know to find equation § How to find the gradient (m) m<0 § How to find the constant c § Straight Line Theory in a Nutshell m=0 y=c § Notice board tips § Self test x=a 9/25/2020 www. mathsrevision. com 2
Standard form for a Straight Line c = y intercept y = mx+c y-axis m = gradient (0, C) m = gradient O x-axis Note : The angle made by the line and the positive x-axis is equal to m = tan( ) 9/25/2020 www. mathsrevision. com 3
Equation of a Straight Line y = mx+c To find the equation of a straight line we need to know Two points that lie on the line ( x 1, y 1) and ( x 2, y 2) Or The gradient and a point on the line m and (a, b) 9/25/2020 www. mathsrevision. com 4
How to find the Gradient m y = mx+c To find the gradient m we need to know 2 point that lie on the straight line. Then use the rule m>0 m<0 m = gradient Gradient can be positive, negative or zero e. g. m=0 y=c What is the gradient of the line passing through the points (3, -5) and (6, 4). Solution x=a 9/25/2020 www. mathsrevision. com 5
How to find constant C y = mx+c To find the constant c, we need to know the gradient m and a point on the line. y = mx+c c = y-mx m = gradient (a, b) = (x, y) (0, C) is were the line crosses the y-axis. e. g. Find the constant c given m = 4 and the point (1, 6). Solution m>0 m<0 (0, C) c=0 m=0 (0, C) Note : If c = 0 then equation is simply 9/25/2020 (0, C) www. mathsrevision. com y = mx 6
Notice Board Tips y is directly proportional to x y = mx+c or y-b= m(x+a) Positive Gradient Negative “If two gradients multiplied together equal -1 then lines are perpendicular” m>0 “Every line cross the y-axis at (0, C)” Gradient m<0 m=0 “If two equations have the same gradient then lines are parallel” y=c line crosses x-axis at y=0 line crosses y-axis at x = 0 , y = c 9/25/2020 x=a www. mathsrevision. com 7
Online Test y = mx+c Q 1. Determine the gradient of the line passing through the points ( 5, 10) and (3, -6) Click here to enter your answer into spreadsheet Q 2. Find the value of the constant “c” for the line in Q 1. above. Use the ALT+TAB keys to navigate to your Spreadsheet and enter answer 9/25/2020 www. mathsrevision. com 8
Online Test Q 3. y = mx+c For the values in Q 1. and Q 2 enter the equation for the line into your spreadsheet (format y=mx+c) Use the ALT+TAB keys to navigate to your Spreadsheet and enter answer Q 4. Find one mathematical word to describe each pair of line equations below. (a) y = 2 x+30 (b) y = -5 x+10 y = 0. 2 x+7 Use the ALT+TAB keys to navigate to your Spreadsheet and enter answer 9/25/2020 www. mathsrevision. com 9
Online Test y = mx+c Q 5. y-axis (4, 9) Find the gradient m. Q 6. Find the constant c. Q 7. Find the equation. Q 8. Find value of angle . (2, 5) O x-axis ( to 1 decimal place) Use the ALT+TAB keys to enter answer into spreadsheet Finally save your spreadsheet, naming it as “name_OTSL” and email to your teacher e. g. 9/25/2020 joebloggs_OTSL www. mathsrevision. com 10
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