Survey
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Material Taken From: Mathematics for the international student Mathematical Studies SL Mal Coad, Glen Whiffen, John Owen, Robert Haese, Sandra Haese and Mark Bruce Haese and Haese Publications, 2004 AND Mathematical Studies Standard Level Peter Blythe, Jim Fensom, Jane Forrest and Paula Waldman de Tokman Oxford University Press, 2012 Vertical and Horizontal Lines All vertical lines have equations of the form x = k where k is a constant. All horizontal lines have equations of the form y = k where k is a constant. Practice 1) Find the equation of the horizontal line that goes through the point (-2, 5) 2) Find the equation of the vertical line that goes through the point (1, -6) y =5 x=1 Graphing Lines Slope-intercept form y = mx + c 1) solve the equation for y. 2) plot the y-intercept 3) use the slope to find another point 4) draw the line x- and y-intercepts Practice Graph using the slope and y-intercept: 1 y x2 3 1) Plot y-intercept = (0, 2) 2) Use slope to plot second point. 1/3 = up 1, to right 3. Thus, (3, 3) 3) Draw line Graphing Lines Slope-intercept form x- and y-intercepts y = mx + c 1) solve the equation for y. 1) find the x-intercept by letting y = 0 2) plot the y-intercept 2) find the y-intercept by letting x = 0 3) use the slope to find another point 3) plot the intercepts. 4) draw the line 4) draw the line Practice Graph by finding the x- and y-intercepts. 2x – 3y – 12 = 0 1) Find x-intercept when y = 0. 2x = 12 or x = 6 2) Plot (6, 0) 3) Find y-intercept when x = 0. 3y = -12 or y = -4 4) Plot (0, -4) 5) Draw line Intersection of Lines Or not … If two lines are parallel then they have the same gradient and do not intersect. Intersection of Lines If two lines L1 and L2 are not parallel then they intersect at just one point. To find intersection point write: m1x1 + c1 = m2x2 + c2 and solve for x. Practice Graph the lines, find where they meet: x+y=6 2x – y = 6 (4, 2) Practice Use your calculator to find where the lines meet: 1) 2) y=x+4 y = 2x + 1 5x – 3y = 0 -x–y=4 (6, 10) (-5/3, -7/3) Practice 1) Find the equation of the perpendicular bisector of AB for A(-1, 2) and B(3, 4) y = -2x + 5 2) Find the equation of the perpendicular bisector of DF for D(4, 0) and F(2, 3) y = 2/3x – 1/2