warm-up solve each equation for y 1) 2) determine if the following points are on the line of the...
TRANSCRIPT
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???