ANSWER y + 4 = 2(x – 6) Daily Homework Quiz Review 5.3 Write an equation in point-slope form of...

ANSWER y + 4 = 2(x – 6)

Daily Homework Quiz

Review 5.3

Write an equation in point-slope form of the line that passes through (6, –4) and has slope 2.

1.

Write an equation in point-slope form of the line that passes through (–1, –6) and (3, 10).

2.

ANSWER y + 6 = 4(x + 1) or y –10 = 4(x–3)

y – y1 = m(x – x1)

€

m =10 − −6

3 − −1=

16

4= 4

Review 5.3

ANSWER

ANSWER

1. (1, 4), (6, –1)

y + 2 = 3(x + 1) or y – 7 = 3(x – 2)

y – 4 = –1(x – 1) or y + 1 = –1(x – 6)

2. (–1, –2), (2, 7)

Write an equation in point-slope form of the line that passes through the given points.

NOW PUT EACH ANSWER IN SLOPE-INTERCEPT FORM!!

y – 4 = – x + 1 or y + 1 = - x + 6

y = – x + 5 or y = - x + 5

+ 4 + 4 - 1 - 1

y + 2 = 3x + 3 or y – 7 = 3x – 6- 2 - 2 + 7 + 7

y = 3x + 1 or y = 3x + 1

€

m =−1 − 4

6 −1=

−5

5= −1

5.4 Write Linear Equations in Standard Form

Convert this equation into standard form:

1.)

€

y =2

5x − 3 Multiply everything by 5

€

5y = 2x −15

-2x -2x

Ax + By = C

€

−2x + 5y = −15

Move over the “x” term

I CAN’T LEAD WITH A NEGATIVE!!!So let’s change the sign of each term.

€

2x − 5y =15 It’s kind of like moving backwards!

Convert this equation into standard form:

2.)

€

y = −x + 5

+ x + x

Ax + By = C

Move over the “x” term

€

x + y = 5

Convert this equation into standard form:

3.)

€

y =−1

2x + 7 Multiply everything by 2

€

2y = −1x +14

+ 1x + 1x

Ax + By = C

Move over the “x” term

€

x + 2y =14

Convert this equation into standard form:

4.)

€

y =2

3x + 4 Multiply everything by 3

€

3y = 2x +12

-2x -2x

Ax + By = C

€

−2x + 3y =12

Move over the “x” term

I CAN’T LEAD WITH A NEGATIVE!!!So let’s change the sign of each term.

€

2x − 3y = −12

Write an equation of the line in STANDARD FORM using the information given.

5.) m = 2 and (3,-2)

Start with Point-Slope Form

€

y − y1 = m(x − x1)

€

y + 2 = 2(x − 3)

Now put into slope-intercept form

€

y + 2 = 2x − 6-2 -2

€

y = 2x − 8-2x -2x

€

−2x + 3y =12

Now put into Standard form

No LEADING NEGATIVES!Change all the signs of each term

€

2x − 3y = −12

Write an equation of the line in STANDARD FORM using the information given.

5.) m = and (4,-5)

Start with Point-Slope Form

€

y − y1 = m(x − x1)

€

y + 5 =3

2(x − 4)

Now put into slope-intercept form

€

y + 5 =3

2x − 6

- 5 - 5

€

y =3

2x −11

- 3x - 3x

€

−3x + 2y = −22

Now put into Standard form

No LEADING NEGATIVES!Change all the signs of each term

€

3x − 2y = 22

€

3

2

Multiply everything by 2

€

2y = 3x − 22

Every one get communicators with a blank side!!!

Write an equation of the line in STANDARD FORM using the information given.

5.) (-4,4) and (0,3)

Start with Point-Slope Form

€

y − y1 = m(x − x1)

€

y − 4 =−1

4(x + 4)

Now put into slope-intercept form

€

y − 4 =−1

4x −1

+ 4 + 4

€

y =−1

4x + 3

+1x +1x

€

x + 4y =12

Now put into Standard form

No LEADING NEGATIVES!Change all the signs of each term

Multiply everything by 4

€

4y = −1x +12

€

m =3 − 4

0 − −4=

−1

4

Write the point-slope form of the line that passes through (4,3) and (1,2)

Write the slope-intercept form of the line that passes through (4,5) and (1,-1)

Write an equation of the line in STANDARD FORM using the information given.

5.) m = -2 and (-4,3)

Start with Point-Slope Form

€

y − y1 = m(x − x1)

€

y − 3 = −2(x + 4)

Now put into slope-intercept form

€

y − 3 = −2x − 8+ 3 + 3

€

y = −2x − 5+ 2x + 2x

€

2x + y = −5

Now put into Standard form

Write an equation of the line in STANDARD FORM using the information given.

5.) m = -3 and (3,-5)

Start with Point-Slope Form

€

y − y1 = m(x − x1)

€

y + 5 =3

2(x − 4)

Now put into slope-intercept form

€

y + 5 =3

2x − 6

- 5 - 5

€

y =3

2x −11

- 3x - 3x

€

−3x + 2y = −22

Now put into Standard form

No LEADING NEGATIVES!Change all the signs of each term

€

3x − 2y = 22

Multiply everything by 2

€

2y = 3x − 22

Write an equation of the line in STANDARD FORM using the information given.

5.) (4,0) and (0,3)

Start with Point-Slope Form

€

y − y1 = m(x − x1)

€

y − 0 =−3

4(x − 4)

Now put into slope-intercept form

€

y =−3

4x + 3

+ 3x + 3x

Now put into Standard form

€

3x + 4 y =12

Multiply everything by 4

€

4y = −3x +12

€

m =3 − 0

0 − 4=

3

−4=

−3

4

Write an equation of the line in STANDARD FORM using the information given.

5.) (2,0) and (0,5)

Start with Point-Slope Form

€

y − y1 = m(x − x1)

€

y − 0 =−5

2(x − 2)

Now put into slope-intercept form

€

y =−5

2x + 5

+ 5x + 5x

Now put into Standard form

€

5x + 2y =10

Multiply everything by 2

€

2y = −5x +10

€

m =5 − 0

0 − 2=

5

−2=

−5

2

SOLUTION

y – y1 = m(x – x1)

Calculate the slope.STEP 1

EXAMPLE 2 Write an equation from a graph

–3m =1 – (–2)

1 – 2=

3–1 =

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

Write point-slope form.

y – 1 = –3(x – 1) Substitute 1 for y1, 3 for m

and 1 for x1.

Write an equation in standard form of the line shown.

STEP 2

Rewrite the equation in standard form.

EXAMPLE 2 Write an equation from a graph

3x + y = 4 Simplify. Collect variable terms on one side, constants on the other.

STEP 3

EXAMPLE 2 Write an equation from a graphGUIDED PRACTICE for Examples 1 and 2

Write an equation in standard form of the line through (3, –1) and (2, –3).

2.

–2x + y = –7ANSWER

Simplify.

Find the value of A. Substitute the coordinates of the given point for x and y in the equation. Solve for A.

STEP 1

SOLUTION

EXAMPLE 4

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

Ax + 3y = 2A(–1) + 3(0) = 2

–A = 2A = –2

Write equation.

Substitute –1 for x and 0 for y.

Divide by –1.

EXAMPLE 3EXAMPLE 4Complete an equation in standard form

EXAMPLE 4Complete an equation in standard form

Complete the equation.

–2x + 3y = 2 Substitute –2 for A.

STEP 2

Write equations of the horizontal and vertical lines that pass through the given point.

GUIDED PRACTICE for Examples 3 and 4

3. (–8, –9)

y = –9, x = –8ANSWER

GUIDED PRACTICE for Examples 3 and 4

4. (13, –5)

y = –5, x = 13ANSWER

Write equations of the horizontal and vertical lines that pass through the given point.

EXAMPLE 4Complete an equation in standard form

Find the missing coefficient in the equation of the line that passes through the given point. Write the completed equation.

EXAMPLE 3 Write an equation of a lineGUIDED PRACTICE for Examples 3 and 4

5. –4x + By = 7, (–1, 1)

ANSWER 3; –4x + 3y = 7

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

4x – 12y = 8

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

SOLUTION

Write two equations in standard form that are equivalent to 2x – 6y = 4.

EXAMPLE 1 Write equivalent equations in standard form

x – 3y = 2

EXAMPLE 1GUIDED PRACTICE for Examples 1 and 2

Write two equations in standard form that are equivalent to x – y = 3.

1.

2x – 2y = 6, 3x – 3y = 9ANSWER

Substitute 0 for s.8(0) + 12l = 144

l = 12

Substitute 0 for l.

s = 188s + 12(0) = 144

ANSWER

The equation 8s + 12l = 144 models the possible combinations.

b. Find the intercepts of the graph.

EXAMPLE 5 Solve a multi-step problem

EXAMPLE 4Complete an equation in standard formEXAMPLE 3 Write an equation of a lineGUIDED PRACTICE for Examples 3 and 4

6. Ax + y = –3, (2, 11)

Find the missing coefficient in the equation of the line that passes through the given point. Write the completed equation.

ANSWER –7; –7x +y = –3