do now 11/18/11 in your notebook, explain if the equations below are the same line. in your...
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Do Now 11/18/11Do Now 11/18/11 In your notebook, explain if the equations below In your notebook, explain if the equations below
are the same line. are the same line.
y – 4 = (x – 1)y – 4 = (x – 1)
y – 1 = (x + 2)y – 1 = (x + 2)
y = 1x + 3y = 1x + 3
y = 1x + 3y = 1x + 3
YESYES
y – 3 = 2(x – 1)y – 3 = 2(x – 1)
y – 1 = 2(x + 2)y – 1 = 2(x + 2)
y = 2x + 1y = 2x + 1
y = 2x + 5y = 2x + 5
NONO
Objective Objective
write linear equations in point-slope form.write linear equations in point-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 change to and is the ratio of the rise change to the run. 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 Equations in “Write Linear Equations in Point-Slope Form”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 (-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-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.
Turkey TriviaTurkey Trivia There are 7 related facts below for this puzzle. After There are 7 related facts below for this puzzle. After
reading all of them, try to figure out the answer to this reading all of them, try to figure out the answer to this question. Who made what?question. Who made what?
(1) Of the five Brady kids, one is named Billy.(1) Of the five Brady kids, one is named Billy. (2) The kids decided to help Mom fix thanksgiving dinner.(2) The kids decided to help Mom fix thanksgiving dinner. (3) Mom fixed the turkey, and the kids divided up the rest of (3) Mom fixed the turkey, and the kids divided up the rest of the work.the work. (4) The boy who prepared the salad wasn’t Ben.(4) The boy who prepared the salad wasn’t Ben. (5) The girl who baked the sweet potatoes wasn’t Bea.(5) The girl who baked the sweet potatoes wasn’t Bea. (6) The kid who cooked the vegetables wasn’t Ben or Betty.(6) The kid who cooked the vegetables wasn’t Ben or Betty. (7) Barbara made the appetizer, not the pumpkin pie.(7) Barbara made the appetizer, not the pumpkin pie.