WARM-UPWARM-UPSolve each equation for y

1)

2)

Determine if the following points are on the line of the equation . Justify your answer.

3) (3, -1)

4) (0, 1)

321 ( 10)

5y x

1 2( 3)y x

1 2( 3)y x

WARM-UPWARM-UPSolve each equation for y1)

2)

Determine if the following points are on the line of the equation . Justify your answer.

3) (3, -1)4) (0, 1)

327

5y x 3

21 ( 10)5

y x

1 2( 3)y x

1 2( 3)y x

2 5y x

YES

NO

NOTES: Writing the NOTES: Writing the equation of a line in point-equation of a line in point-slope form Day 1slope form Day 1

AlgebraAlgebra

Let’s remember the different slopes possible…

Positive Slope

x

y

m > 0

Line rises from left to right.

Zero Slope

x

y

m = 0

Line is horizontal.m is

undefined

Undefined Slope

x

y

Line is vertical.

Negative Slope

x

y

m < 0

Line falls from left to right.

Point-Slope Form of the Equation of a Line

The point-slope equation of a non-vertical line of slope m that passes through the point (x1, y1) is

y – y1 = m(x – x1).

The point-slope equation of a non-vertical line of slope m that passes through the point (x1, y1) is

y – y1 = m(x – x1).

Point Slope Formula

The point-slope formula

y – y1 = m(x – x1).

m = slope

The point-slope formula

y – y1 = m(x – x1).

m = slope

1 1( , ) pointx y

Example 1Example 1

• Write an equation of the line in point-slope form that passes through the given point and has the given slope: m = –8, (7, –7)

Step 1: Write down the formula

1 1( )y y m x x

Example 1Example 1

• Write an equation of the line in point-slope form that passes through the given point and has the given slope: m = –8, (7, –7)

Step 2: Substitute the given slope

1 1( )y y m x x

1 18( )y y x x

Example 1Example 1

• Write an equation of the line in point-slope form that passes through the given point and has the given slope: m = –8, (7, –7)

Step 3: Substitute the given point

1 18( )y y x x ( 7) 8( (7))y x

Example 1Example 1

• Write an equation of the line in point-slope form that passes through the given point and has the given slope: m = –8, (7, –7)

Step 4: Simplify

( 7) 8( (7))y x 7 8( 7)y x

Column Questions???

Example 2Example 2

• Write an equation of the line in point-slope form that passes through the given point and has the given slope: m = 4, (3, 1)

Step 1: Write down the formula

1 1( )y y m x x

Example 2Example 2

• Write an equation of the line in point-slope form that passes through the given point and has the given slope: m = 4, (3, 1)

Step 2: Substitute the given slope

1 1( )y y m x x

1 14( )y y x x

Example 2Example 2

• Write an equation of the line in point-slope form that passes through the given point and has the given slope: m = 4, (3, 1)

Step 3: Substitute the given point

1 14( )y y x x (1) 4( (3))y x

Example 2Example 2

• Write an equation of the line in point-slope form that passes through the given point and has the given slope: m = 4, (3, 1)

Step 4: Simplify

(1) 4( (1))y x 1 4( 3)y x

Column Questions???

Example 3: Writing the Point-Slope Equation of a Line YOU TRY!!

Write the point-slope form of the equation of the line passing through (-1,2) with a slope of 4. Then solve the equation for y.

Solution We use the point-slope equation of a line with m = 4 and (-1, 2).

This is the point-slope form of the equation.y – y1 = m(x – x1)

Substitute the given values. Simplify.y – 2 = 4[x – (-1)]

We now have the point-slope form of the equation for the given line.

y – 2 = 4(x + 1)

Y – 2 = 4x + 4

Y = 4x + 6Solve for y. This is called slope-intercept form.

Example 4: Writing the Point-Slope Equation of a Line YOU TRY!!

Write the point-slope form of the equation of the line passing through (-5,-2) with a slope of -4. Then solve the equation for y.

Solution We use the point-slope equation of a line with m = -4 and (-5, -2).

This is the point-slope form of the equation.y – y1 = m(x – x1)

Substitute the given values. Simplify.y – (-2 )= -4[x – (-5)]

We now have the point-slope form of the equation for the given line.

y + 2 = -4(x + 5)

Summary and Column Questions???