Unit 1 Lesson 3 part a 9172014 Warmup 1 Find the slope given two points 2 1 and 5 3 2 Solve for x in the equation Ax By C SlopeIntercept Form y mx b x and y x y coordinate ID: 601834
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Slide1
Slope Intercept Form
Unit 1, Lesson 3 part a
9/17/2014Slide2
Warmup
1. Find the slope given two points (-2, 1) and (5, -3).
2
. Solve for x in the equation Ax + By = C.Slide3
Slope-Intercept Form:
y = mx + b
x and y: (x, y) coordinate
m: slope
b: y-intercept (Where the line crosses the y-axis)
To graph a linear equation, we need the slope (m) and y-intercept (b)Terminology of Slope-Intercept Form: *Slope: *Y-Intercept: Coefficient of x Constant Variable TermSlide4
Graph y = 5x – 2
m: 5 ---->
b: (0, -2)
Start at the y-intercept
(0, -2)
Up or Down?
up 5 -- right 1
or down 5 -- left 1YOU MUST GRAPH AT LEAST FOUR POINTS!!! USE A STRAIGHT EDGE!!!
Slide5Slide6
Graph y = -
x
m: -
or
or
b: (0, 0)
Start at the y-intercept
(0, 0)
Up or Down?
down 3 -- right 2
or
up 3 -- left 2
YOU MUST GRAPH AT LEAST FOUR POINTS!!! USE A STRAIGHT EDGE!!!
Slide7Slide8
Graph y = 3 -
x
m: -
b: (0, 3)
Start at the y-intercept
(0, 3)
Up or Down?
down 1 -- right 2
or
up 1 -- left 2
YOU MUST GRAPH AT LEAST FOUR POINTS!!! USE A STRAIGHT EDGE!!!
Slide9Slide10
Graph y = x +
m: 1 --->
b: (0,
)
Start at the y-intercept
(0,
)
Up or Down?
up 1 -- right 1
or
down 1 -- left 1
YOU MUST GRAPH AT LEAST FOUR POINTS!!! USE A STRAIGHT EDGE!!!
Slide11Slide12
Special Cases: Thought Process...
x =
constant
crosses
the x-axis
vertical line undefined slopey = constant crosses the y-axis horizontal linezero slopeSlide13
Exit Ticket
Find the slope and graph the equation of
. Slide14
Standard form of a line
Unit 1, Lesson 3 part b
9/18/2014Slide15
Warmup
1. Write an equation of the given line.
2. Draw the graph of y = -2x + 5
3. What operation should be performed first when solving
Slide16
Writing the equation of a line in standard form
A line is in STANDARD FORM when it is written as:
Ax + By = C
Note: both A, B, and C must all be integers and A MUST be positive!
Standard form is the same equation as a line in slope-intercept form, it’s just written differentlySlide17
Converting from slope-intercept to standard form
Recall that the slope-intercept form of a line is: y = mx + b.
To
change this into standard form, we start
by:
1. Moving the x-term to the left side of the equation. This is done by subtracting mx from both sides. We now have the equation, -mx + y = b. 2. The coefficient of the x-term should be a positive integer. So we multiply the entire equation by an integer that will make that coefficient positive. 3. Whatever number you have multiplied the coefficient of x by, multiply that number with
all of the
other terms as well.
This gives us the standard form: Ax + By = CSlide18
Example #1
Write the equation of the line: y = -3x + 6 in standard
form.Slide19
Example #2
Write the equation of the line: y = 2x + 7 in standard form.Slide20
Example #3
Write the equation of the line: y = (1/2)x + 8 in standard
form.Slide21
Example #4
Write the equation of the line
that
passes through the point (0,6)
and (-2, -2) in
standard form.