LINEAR EQUATIONS PART I

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LINEAR EQUATIONS PART I

1. Basic Coordinate Plane Info
2. Review on Plotting Points
3. Finding Slopes
4. x and y intercepts
5. Slope-Intercept Form of a Line
6. Graphing Lines
7. Determine the equation of a line given two
   points, slope and one point, or a graph.

Assignments
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COORDINATE PLANE
Y-axis

• Parts of a plane
• X-axis
• Y-axis
• Origin
• Quadrants I-IV

QUAD I
QUAD II
Origin ( 0 , 0 )
X-axis
QUAD III
QUAD IV
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PLOTTING POINTS
Remember when plotting points you always start at
the origin. Next you go left (if x-coordinate is
negative) or right (if x-coordinate is positive.
Then you go up (if y-coordinate is positive) or
down (if y-coordinate is negative)
B
C
Plot these 4 points A (3, -4), B (5, 6), C (-4,
5) and D (-7, -5)
A
D
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SLOPE
Slope is the ratio of the vertical rise to the
horizontal run between any two points on a line.
Usually referred to as the rise over run.
Slope triangle between two points. Notice that
the slope triangle can be drawn two different
ways.
Run is 6 because we went to the right
Rise is 10 because we went up
Rise is -10 because we went down
Run is -6 because we went to the left
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FORMULA FOR FINDING SLOPE
The formula is used when you know two points of a
line.
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Find the slope of the line between the two points
(-4, 8) and (10, -4)
If it helps label the points.
Then use the formula
slope
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X AND Y INTERCEPTS
The x-intercept is the x-coordinate of a point
where the graph crosses the x-axis.
The y-intercept is the y-coordinate of a point
where the graph crosses the y-axis.
The x-intercept would be 4 and is located at the
point (4, 0).
The y-intercept is 3 and is located at the point
(0, 3).
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SLOPE-INTERCEPT FORM OF A LINE
The slope intercept form of a line is y mx b,
where m represents the slope of the line and
b represents the y-intercept.
When an equation is in slope-intercept form the
y is always on one side by itself. It can not
be more than one y either.
If a line is not in slope-intercept form, then we
must solve for y to get it there.
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IN SLOPE-INTERCEPT NOT IN SLOPE-INTERCEPT
y 3x 5 y x 10
y -2x 10 2y 8 6x
y -.5x 2 y 4 2x
Put y x 10 into slope-intercept form
Add x to both sides
and would get y x 10
Put 2y 8 6x into slope-intercept form.
Add 8 to both sides then
divide by 2 and would get y 3x 4
Put y 4 2x into slope-intercept form.
Subtract 4 from both sides
and would get y 2x 4.
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GRAPHING LINES

• BY MAKING A TABLE OR USING THE SLOPE-INTERCEPT
  FORM

I could refer to the table method by input-output
table or x-y table. For now I want you to include
three values in your table. A negative number,
zero, and a positive number.
Graph y 3x 2
INPUT (X) OUTPUT (Y)
-2 -4
0 2
1 5
By making a table it gives me three points, in
this case (-2, -4) (0, 2) and (1, 5) to plot and
draw the line.
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Plot (-2, -4), (0, 2) and (1, 5)
Then draw the line. Make sure your line covers
the graph and has arrows on both ends. Be sure to
use a ruler.
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Slope-intercept graphing

• Steps
• Make sure the equation is in slope-intercept
  form.
• Identify the slope and y-intercept.
• Plot the y-intercept.
• From the y-intercept use the slope to get another
  point to draw the line.

• y 3x 2
• Slope 3 (note that this means the fraction or
  rise over run could be (3/1) or (-3/-1). The
  y-intercept is 2.
• Plot (0, 2)
• From the y-intercept, we are going rise 3 and run
  1 since the slope was 3/1.

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FIND EQUATION OF A LINE GIVEN 2 POINTS
Find the equation of the line between (2, 5) and
(-2, -3).

1. Slope is 2.
2. y 2x b
3. Picked the point (2, 5) to substitute into the
   formula
4. so (5) 2(2) b
5. b 1
6. y 2x 1

• STEPS
• Find the slope between the two points.
• Plug in the slope in the slope-intercept form.
• Pick one of the given points and plug in numbers
  for x and y.
• Solve and find b.
• Rewrite final form.

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FIND EQUATION OF A LINE GIVEN A POINT and SLOPE
Find the equation of the line through (2, 5)
with a slope of - 5

1. Slope is -5.
2. y -5x b
3. Picked the point (2, 5) to substitute into the
   formula
4. so (5) -5(2) b
5. b 15
6. y -5x 15

• Steps
• Substitute the slope into the slope-intercept
  form.
• Use the point to plug in for x and y.
• Find b.
• Rewrite equation.

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FIND EQUATION OF A LINE GIVEN A GRAPH

• If given a graph there are three ways.
• One way is to find two points on the line and use
  the first method we talked about.
• Another would be to find the slope and pick a
  point and use the second method.
• The third method would be to find the slope and
  y-intercept and plug it directly into y mx b.