Download Math 10 Linear Functions Review

Math 10 Linear Functions Review
y  mx  b
is the general equation of a linear function
m = slope
ex.
y
x
y  y1
m= 2
x2  x1
m=
m=
The slope of the line that passes through
(2,1) and (-3,0)
y
x
m=
y 2  y1
x2  x1
m=
◊ Horizontal Lines have a slope of zero!
4
0 1
32
m=
Ex. y  3
y
3
2
1
x
–4
–3
–2
–1
1
2
3
4
–1
–2
–3
–4
◊ Vertical Lines have an undefined slope
4
Ex. x  2
y
3
2
1
x
–4
–3
–2
–1
1
–1
–2
–3
–4
2
3
4
1
5
m=
1
5
◊ Parallel Lines have equal slopes
4
y
3
2
1
x
–7
–6
–5
–4
–3
–2
–1
1
2
3
4
5
6
7
–1
–2
–3
–4
◊ Perpendicular Lines have negative reciprocal slopes
4
y
3
2
1
x
–7
–6
–5
–4
–3
–2
–1
1
2
3
4
5
6
–1
–2
–3
–4
◊ Positive slopes have graphs that rise to the right
4
y
3
2
1
x
–7
–6
–5
–4
–3
–2
–1
1
–1
–2
–3
–4
2
3
4
5
6
7
7
◊ Negative slopes have graphs that decrease to the right
4
y
3
2
1
x
–6
–4
–2
2
4
6
–1
–2
–3
–4
From y = mx + b, “b” is the y-intercept (0, b)
ex. For y = -3x + 1
4
y
3
b = 1, so the y-intercept is (0,1)
2
1
x
–6
–4
–2
2
4
6
–1
–2
y-intercept
(0,1)
–3
–4
Finding the intercepts (where the graph crosses the x and y axes)
x-intercept (let y = 0)
y-intercept (let x = 0)
ex. What is the x-intercept of the linear function
y  3x  2 ?
0 = 3x - 2
2 = 3x
3 3
2/3 = x
x-int. (2/3, 0)
ex. What is the y-intercept of the linear function
y  2x  1?
Y = 2(0) + 1
Y=0+1
Y=1
y-int. (0, 1)
Point-Slope Equation is useful
y  y1  m( x  x1 )
Ex. Find the equation of a line that has a slope of 2 and passes through (1, 3)
y  3  2( x  1)
Graphing using the Intercept method (x, 0) and (0, y)
Given an equation not in the General Form, the intercept method is a useful way of
graphing (without having to rearrange the equation)
Ex. Graph -4x + 1 = 2y -3
The x-intercept can be found when y = 0.
-4x + 1 = 2(0) – 3
-4x + 1 = -3
-4x = -3-1
-4x = -4
4
4
x=1
The y-intercept can be found when x = 0.
-4(0) + 1 = 2y – 3
1 = 2y – 3
1 + 3 = 2y
4 = 2y
2 2
2=y
x-intercept is (1, 0)
y-intercept is (0, 2)
4
y
3
2
1
x
–6
–4
–2
2
–1
–2
–3
–4
4
6
Finding and Equation given…
(a)
(b)
(c)
(d)
(e)
(f)
two points
slope and one point
slope and the y-intercept (a point)
slope and the x-intercept (a point)
Parallel or Perpendicular to another line and a point
The graph (visually)
Note - Remember that you know how to move variables and numbers from one side
of the equation to the other. You can solve for y if the equation is not in the
general equation of y=mx+b