Do Now 11/20/09Do Now 11/20/09Take out HW from last night.Take out HW from last night.– 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

Copy HW in your planner.Copy HW in your planner.– Text page 314, #8-16 evens, 26-36 evensText page 314, #8-16 evens, 26-36 evens– Mid-Chapter 5 Quiz TuesdayMid-Chapter 5 Quiz Tuesday

In your journal, explain if the equations below are the In your journal, explain if the equations below are the same line. 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

HomeworkHomework Text. page 305, #6, 8, 12, 14, 16, 20, 22, 24, 26, 32 Text. page 305, #6, 8, 12, 14, 16, 20, 22, 24, 26, 32

6) y + 1 = -2(x – 5) 6) y + 1 = -2(x – 5) 8) y – 6 = 3/2(x + 6)8) y – 6 = 3/2(x + 6)12) C12) C14) graph: start @ (1,5), use slope of 3. 14) graph: start @ (1,5), use slope of 3. 16) graph: start @ (-6,1), use slope of 3.16) graph: start @ (-6,1), use slope of 3.20) y – 1 = 2(x – 3) or y + 3 = 2(x – 1) 20) y – 1 = 2(x – 3) or y + 3 = 2(x – 1) 22) y – 4 = -1/2(x + 5) or y – 2 = -1/2(x + 1) 22) y – 4 = -1/2(x + 5) or y – 2 = -1/2(x + 1) 24) y + 2 = ½(x – 6) or y – 1 = ½(x – 12) 24) y + 2 = ½(x – 6) or y – 1 = ½(x – 12) 26) y – 5 = 5/4(x – 4) or y + 5 = 5/4(x + 4) 26) y – 5 = 5/4(x – 4) or y + 5 = 5/4(x + 4) 32) Yes, because the rate of change is increasing at a 32) Yes, because the rate of change is increasing at a constant rate. y – 1.2 = 1/5(x – 1) constant rate. y – 1.2 = 1/5(x – 1)

Objective Objective

SWBAT write linear equations in SWBAT write linear equations in standard form.standard form.

Section 5.4 Section 5.4 “Write Linear “Write Linear Equations in Standard Form”Equations in Standard Form”

The The STANDARD FORMSTANDARD FORM of a of a linear equation is represented aslinear equation is represented as

AAx x ++ BBy y = C= Cwhere A, B, and C are real where A, B, and C are real

numbersnumbers

To write another equivalent equation, multiply each side by 0.5.

4x – 12y = 8

To write one equivalent equation, multiply each side by 2.

SOLUTIONSOLUTION

Write two equations in standard form thatWrite two equations in standard form thatare equivalent to are equivalent to 22x x – 6– 6y y == 4.4.

x – 3y = 2

y y – – yy11 = = mm((x x – – xx11))

Calculate the slope.Calculate the slope.STEPSTEP 11

–– 33mm == 1 – (–2)1 – (–2) 1 –21 –2 ==

33––11 ==

Write an equation in point-slope form. Use Write an equation in point-slope form. Use (1, 1).(1, 1).

Write point-slope form.Write point-slope form.

y y – 1 = – 3(– 1 = – 3(x x – 1)– 1) Substitute Substitute 11 for for yy11,, - -33 for for mm and and 11 for for xx11..

Write an equation in standard form of the line shown.Write an equation in standard form of the line shown.

STEPSTEP 22

Rewrite the equation in standard form.Rewrite the equation in standard form.

33x x + + y y = 4= 4 Simplify. Collect variable terms on Simplify. Collect variable terms on one side, constants on the other.one side, constants on the other.

STEPSTEP 33

y y – – yy11 = = mm((x x – – xx11))

Calculate the slope.Calculate the slope.STEPSTEP 11

22mm == -3 – (–1)-3 – (–1) 2 –32 –3 ==

-2-2 -1-1 ==

Write an equation in point-slope form. Use Write an equation in point-slope form. Use (3, -1).(3, -1).

Write point-slope form.Write point-slope form.

STEPSTEP 22

Rewrite the equation in standard form.Rewrite the equation in standard form.

-2x -2x + + y y = -7= -7 Simplify. Collect variable terms on Simplify. Collect variable terms on one side, constants on the other.one side, constants on the other.

STEPSTEP 33

Write an equation in standard form of the line that passes through the points (3, -1) and (2, -3).

y + 1 = 2(x – 3) Substitute 3 for x1, –1 for y1 and 2 for m.

SOLUTIONSOLUTION

Write an equation of the specified line.Write an equation of the specified line.

The The yy--coordinate of the given point on the blue coordinate of the given point on the blue line is line is –4. –4. This means that all points on the line This means that all points on the line have a have a yy--coordinate of coordinate of –4.–4. An equation of the An equation of the line is line is yy == –4.–4.

aa..

The The xx--coordinate of the given point on the red coordinate of the given point on the red line is line is 4.4. This means that all points on the line This means that all points on the line have an have an xx--coordinate of coordinate of 4.4. An equation of the An equation of the line is line is xx = 4.= 4.

bb..

Blue lineBlue lineaa. . Red lineRed linebb. .

SOLUTION

The y-coordinate of the given point is –5. This means that all points on the line have a y-coordinate of –5. An equation of the line is y = –5.

The x-coordinate of the given point is 13. This means that all points on the line have an x-coordinate of 13. An equation of the line is x = 13.

Write an equation of the horizontal and vertical lines that pass through the given point. (13, –5)

STEP 1

STEP 2

Simplify.Simplify.

Find the value of Find the value of AA. Substitute the coordinates . Substitute the coordinates of the given point for of the given point for xx andand yy in the in the equation. Solve forequation. Solve for AA..

STEPSTEP 11

SOLUTIONSOLUTION

Find the missing coefficient in the equation of the line Find the missing coefficient in the equation of the line shown. Write the completed equationshown. Write the completed equation..

Ax Ax + 3+ 3y y = 2= 2AA(–1) + 3(0) = 2(–1) + 3(0) = 2

––A A = 2= 2A A = – 2= – 2

Write equation.Write equation.Substitute Substitute – 1– 1 for for x x and and 00 for for yy..

Divide by Divide by – – 1.1.

Complete an equation in Complete an equation in standard formstandard form

Complete the equation.Complete the equation.

– – 22x x + 3+ 3y y = 2= 2 Substitute – Substitute – 2 2 for for AA..

STEPSTEP 22

Find the missing coefficient in the equation of the line Find the missing coefficient in the equation of the line that passes through the given point. Write the that passes through the given point. Write the completed equationcompleted equation.. Ax + y = –3, (2, 11)

Simplify.Simplify.

Find the value of Find the value of AA. Substitute the coordinates . Substitute the coordinates of the given point for of the given point for xx andand yy in the in the equation. Solve forequation. Solve for AA..

STEPSTEP 11

Ax Ax + + y y = -3= -3AA(2) + (11) = -3(2) + (11) = -3

2A 2A = -14= -14A A = –7= –7

Write equation.Write equation.Substitute 2 for Substitute 2 for x x and 11 for and 11 for yy..

Divide by 2Divide by 2..

Complete the equation.Complete the equation.STEPSTEP 22

– 7x +y = –3 Substitute Substitute –7–7 for for AA..

2424

HomeworkHomework– Text page 314, #8-16, 26-36 evensText page 314, #8-16, 26-36 evens– Mid-Chapter 5 Quiz TuesdayMid-Chapter 5 Quiz Tuesday