Download Material Taken From: Mathematics for the international student

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  x2
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