FACTS about a Linear Equations/Lines:
1.
Has one or two variables
2.
No variable in a linear equation is raised to a power
greater than 1 or used as the denominator of a fraction.
examples of linear equations:
x=­3
y = 1/3x ­ 4
y= 5
2x + 7y = 12
4y = 2x + 8
examples of non­linear equations: y = x2 + 3x
y= 5
x
3. Any two points determine a line
4. When you find points or pairs of values (x , y) that make
the linear equation true and plot those pairs on a
coordinate plane, all of the points lie on the same line.
5. Linear equations are straight lines when graphed.
6. In a linear equation in two variables, x and y, the value of
one of the variables depends on the value of the other
variable
x is the independent variable
y is the dependent variable
v
The graph at the right shows the line
y = x + 2
Does the point (2 , 4) lie on the line?
Does the point (4, 2) lie
v
on the line?
Does the point ( 3, ­3 ) lie on the line
y = 2x + 3 ?
Does the point (­3 , 5) lie on the line y = 2x + 11 ?
The SLOPE of a line tells two things:
1. how steep the line is
2. whether the line slopes up or down when you look at
it from left to right
SLOPE on Graphs
SLOPE = y­change
run
rise +
+6
rise
x­change
= rise
run
y
­
+4
run
slope = 4 = 2
3
6
x
rises UPward
­
+
NEGATIVE SLOPE
falls DOWNward
slope = ­3
4
­3
+4
SLOPE
SLOPE a.k.a RATE OF CHANGE
Slope is the rate at which y is changing with respect to the change in x Pick any two points on the line:
To find how fast y is changing, subtract the y value of the
second point from the y value of the first point (y2 – y1)
To find how fast x is changing, subtract the x value of the
second point from the x value of the first point (x2 – x1)
Given any 2 points on a line ( x1 , y1 ) and ( x2 , y2 ) :
SLOPE = change in y values =
(m)
change in x values
m
=
(y2 – y1)
(x2 – x1)
x
y
­2
5
­1
3
0
1
1
­1
Find the slope of the line represented in the table
y­intercept graph
• Where a straight line crosses
the y axis of a graph
• It occurs when x­value is 0
• Coordinates of the y­intercept
are (0, y)
table
x­intercept
• Where a straight line crosses
the x axis of a graph
• It occurs when y­value is 0
• Coordinates of the y­intercept
are (x, 0)
table
graph
v
y­intercept:______
v
x­intercept:____
slope:_____ SLOPE ­ INTERCEPT FORM: EQUATION OF A LINE
Graphing equations in Slope­Intercept form:
STEP 4: Connect the points to form line (use RULER and don't be cheap!)
y = 2x ­ 5
y = ­ 2
3
x
+ 4
Graph the following linear equations
***** (put into y = mx + b form first) *****
1.
x + y = ­ 2
2. 5y = 10x + 25
3. 4x ­ y = 8
EQUATION:
y = m x + b
y = 4 x ­ 4
3
v
y ­intercept:______
v
slope:_____ equation: _______________
V
y ­intercept:______
slope:_____ equation: _______________
V