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

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. Vertical and Horizontal Lines

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) Practice y = 5x = 1

Graphing Lines x- and y-intercepts 1) solve the equation for y. 4) draw the line Slope-intercept form 2) plot the y-intercept 3) use the slope to find another point y = mx + c

Graph using the slope and y-intercept: Practice 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

1) find the x-intercept by letting y = 0 2) find the y-intercept by letting x = 0 3) plot the intercepts. x- and y-intercepts 1) solve the equation for y. 4) draw the line Slope-intercept form 2) plot the y-intercept 3) use the slope to find another point 4) draw the line y = mx + c Graphing Lines

Graph by finding the x- and y-intercepts. 2x – 3y – 12 = 0 Practice 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 L 1 and L 2 are not parallel then they intersect at just one point. To find intersection point write: m 1 x 1 + c 1 = m 2 x 2 + c 2 and solve for x.

x + y = 6 2x – y = 6 Graph the lines, find where they meet: Practice (4, 2)

1) y = x + 4 5x – 3y = 0 Use your calculator to find where the lines meet: Practice 2) y = 2x x – y = 4 (6, 10)(-5/3, -7/3)

1) Find the equation of the perpendicular bisector of AB for A(-1, 2) and B(3, 4) 2) Find the equation of the perpendicular bisector of DF for D(4, 0) and F(2, 3) Practice y = -2x + 5 y = 2/3x – 1/2