Do Now 11/19/09 Take out HW from last night. –Text. page 296, #4-28 multiples of 4, #30-46 every 4...
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Transcript of Do Now 11/19/09 Take out HW from last night. –Text. page 296, #4-28 multiples of 4, #30-46 every 4...
Do Now 11/19/09Do Now 11/19/09
Take out HW from last night.Take out HW from last night.– Text. page 296, #4-28 multiples of 4, #30-46 every 4Text. page 296, #4-28 multiples of 4, #30-46 every 4
Copy HW in your planner.Copy HW in your planner.– Text. page 305, #6, 8, 12, 14, 16, 20, 22, 24, 26, 32Text. page 305, #6, 8, 12, 14, 16, 20, 22, 24, 26, 32– Mid-Chapter 5 Quiz next WednesdayMid-Chapter 5 Quiz next Wednesday
In your journal, list the 3 steps you have to take in order to In your journal, list the 3 steps you have to take in order to write the equation of a line when you know two points on write the equation of a line when you know two points on that line. Then write the equation of the line containing that line. Then write the equation of the line containing the following points: (10,-5), (-5, 1)the following points: (10,-5), (-5, 1)
15
2 xy
HomeworkHomeworkText p. 296, #4-28 multiples of 4, #30-46 every 4 Text p. 296, #4-28 multiples of 4, #30-46 every 4
4) y = 2x – 9 4) y = 2x – 9
8) y = 1/2x – 19/2 8) y = 1/2x – 19/2
12) y = 7x – 19 12) y = 7x – 19
16) y = -1/2x – 7/4 16) y = -1/2x – 7/4
20) y = -7/6x + 11/6 20) y = -7/6x + 11/6
24) y = -x – 4 24) y = -x – 4
28) y = -3x – 6 28) y = -3x – 6
30) y = -1/4x + 530) y = -1/4x + 5
34) Yes34) Yes
38) y = 3/2x – 1/2 38) y = 3/2x – 1/2
42) Yes; y = 3/4x + 142) Yes; y = 3/4x + 1
46) 7; find the 46) 7; find the equation of the line equation of the line through (-2,3) and through (-2,3) and (2,5) to be y = 1/2x + (2,5) to be y = 1/2x + 4, then substitute 6 for 4, then substitute 6 for x to find k. x to find k.
ObjectiveObjective
SWBAT write linear equations in point-SWBAT write linear equations in point-slope form.slope form.
Slope ReviewSlope Review
The slope The slope m m of a line passing through two pointsof a line passing through two points
and is the ratio of the rise and is the ratio of the rise change to the run. change to the run.
),( 11 yx ),( 22 yx
m
y
x
),( 11 yx
),( 22 yx
runrun
riserise)( 12 yy
)( 12 xx
Section 5.3 Section 5.3 “Write Linear “Write Linear Equations in Point-Slope Form”Equations in Point-Slope Form”
POINT-SLOPE FORM-POINT-SLOPE FORM-
of a linear equation is written as:of a linear equation is written as:
slope
y-coordinatepoint 1
x-coordinatepoint 1
)( 11 xxmyy
y
x
),( 11 yx
),( yx
runrun
riserise
Write an equation in point-slope form of the line that passes through the point (4, -3) and has a slope of 2.
Write point-slope form.Write point-slope form.
Substitute 2 for Substitute 2 for mm, 4, 4 for for x,x, and - and -33 for for yy..
Write point-slope formSTEP 1
Substitute for the slope and the coordinates of the given point in
STEP 2
Write in point-slope.Write in point-slope.
Write an equation of the line in point-slope form.STEP 3
)( 11 xxmyy
)( 11 xxmyy
)4(23 xy
)4(23 xy
Write an equation in point-slope form of the line that passes through the point (-1, 4) and has a slope of -2.
Write point-slope form.Write point-slope form.
Substitute -2 for Substitute -2 for mm, -1, -1 for for x,x, and and 4 for 4 for yy..
Write point-slope formSTEP 1
Substitute for the slope and the coordinates of the given point in
STEP 2
Write in point-slope.Write in point-slope.
Write an equation of the line in point-slope form.STEP 3
)( 11 xxmyy
)( 11 xxmyy
)1(24 xy
)1(24 xy
Write an equation in point-slope formWrite an equation in point-slope form of the line that of the line that passes through passes through (2, 3)(2, 3) andand (4, 4).(4, 4).
m = y2 – y1x2 – x1
= 4 – 3 4 – 2
= 12
Calculate the slope. STEP 1
Write point-slope form.Write point-slope form.
Substitute for the slope and the coordinates of the given point in
STEP 2)( 11 xxmyy
)( 11 xxmyy
)4(2
14 xy )2(
2
13 xyor
Write an equation in point-Write an equation in point-slope formslope form of the line shownof the line shown..
m = y2 – y1x2 – x1
= 3 – 1 -1– 1
= 2-2
Calculate the slope. STEP 1
Write point-slope form.Write point-slope form.
Substitute for the slope and the coordinates of the given point in
STEP 2)( 11 xxmyy
)( 11 xxmyy
)1(13 xy )1(11 xy
y
x
)3,1(
)1,1(
= -1
or
Graph the equation.Graph the equation.
)3(3
22 xy
Because the equation is in point-slope form, you know that the line has a slope of and passes through the point (3, –2).
2 3
Plot the point (3, – 2). Find a second
point on the line using the slope.
Draw a line through both points.
Graph the equation.Graph the equation.
)2(1 xy
Because the equation is in point-slope form, you know that the line has a slope of –1 and passes through the point (2, 1).
Plot the point (2, 1). Find a second point on the line using the slope. Draw a line through both points.
What Did We Learn Today? What Did We Learn Today?
POINT-SLOPE FORM-POINT-SLOPE FORM-
of a linear equation is written as:of a linear equation is written as:
slope
y-coordinatepoint 1
x-coordinatepoint 1
)( 11 xxmyy
y
x
),( 11 yx
),( yx
runrun
riserise
2424
HomeworkHomework
Text page 305, #6, 8, 12, 14, 16, 20, 22, 24, 26, 32Text page 305, #6, 8, 12, 14, 16, 20, 22, 24, 26, 32