Bell Ringer
Is the data in
the table
linear?
Write an equation in
Point Slope Form
(1,2) ; m undefined
x=1
No, Data IS NOT Linear
Today’s Objectives
Write equations in standard form.
Write equations of lines that are parallel or perpendicular
to another line.
Standard Form
Ax + By = c
Where A,B,C are expressed as integers, and A & B are both not zero.
y=x-3
Get x and y on the same side
-x + y = -3
Get rid of all fractions by rationalizing the denominator
-x + y = -3
Standard Form
Ax + By = c
Where A,B,C are expressed as integers, and A & B are both not zero.
3y = 2x + 6
Get x and y on the same side
-2x + 3y = 6
Get rid of all fractions by rationalizing the denominator
-2x + 3y = 6
Standard Form
Ax + By = c
Where A,B,C are expressed as integers, and A & B are both not zero.
y = 2/3 x + 25/3
Get x and y on the same side
-2/3 x + y = 25/3
Get rid of all fractions by rationalizing the denominator
-2x + 3y = 25
Standard Form
Ax + By = c
Where A,B,C are expressed as integers, and A & B are both not zero.
2y = -5/2 x + 7/3
Get x and y on the same side
5/2 x + 2y = 7/3
Get rid of all fractions by rationalizing the denominator
15x + 12y = 14
Parallel Lines
Two or more lines that are the same distance
apart everywhere. They also have no
points in common
Parallel Lines
 Same Slopes
 Different Y-Intercepts
Write the equation of a line that is parallel to y = 3x + 8 and
Passes through the point (2,1)
What is the slope of the parallel line?
m=3
Use Point-Slope form to find the equation.
m=3
(2,1)
y – y1 = m(x – x1)
y – 1 = 3(x – 2)
Write answer in Slope-Intercept Form.
y – 1 = 3x – 6
y = 3x – 5
Parallel Lines
Write the equation of a line that is parallel to 2y = 4x + 7 and
Passes through the point (3,6)
What is the slope of the parallel line?
2y = 4x + 7
m=2
y = 2x + 7/2
Use Point-Slope form to find the equation.
m=2
(3,6)
y – y1 = m(x – x1)
y – 6 = 2(x – 3)
Write answer in Slope-Intercept Form.
y – 6 = 2x – 6
y = 2x
Parallel Lines
Write the equation of a line that is parallel to 3y = 5x + 2 and
Passes through the point (1,1)
What is the slope of the parallel line?
= 5x + 2
m = 5/3 3y
y = 5/3 x + 2/3
Use Point-Slope form to find the equation.
m = 5/3 (1,1)
y – y1 = m(x – x1)
y – 1 = 5/3(x – 1)
Write answer in Slope-Intercept Form.
y – 1 = 5/3x – 5/3
y = 5/3x – 2/3
Perpendicular Lines
Two lines that intersect to form right angles (90°),
which are also referred to as normal angles
Parallel Lines
 Negative Reciprocal Slopes
 Different Y-Intercepts
Write the equation of a line that is perpendicular to y = 3x + 8 and
Passes through the point (2,1)
What is the slope of the perpendicular line?
m = -1/3
Use Point-Slope form to find the equation.
m = -1/3 (2,1)
y – y1 = m(x – x1)
y – 1 = -1/3(x – 2)
Write answer in Slope-Intercept Form.
y – 1 = -1/3x + 2/3
y = -1/3x + 5/3
Parallel Lines
Write the equation of a line that is perpendicular to 2y = 4x + 7 and
Passes through the point (6,6)
What is the slope of the perpendicular line?
= 4x + 7
m = -1/2 2y
y = 2x + 7/2
Use Point-Slope form to find the equation.
m = -1/2 (6,3)
y – y1 = m(x – x1)
y – 3 = -1/2(x – 6)
Write answer in Slope-Intercept Form.
y – 3 = -1/2x + 3
y = -1/2x + 6
Parallel Lines
Write the equation of a line that is perpendicular to 3y = -x + 2 and
Passes through the point (1,1)
What is the slope of the perpendicular line?
3y = -x + 2
m=3
y = -1/3 x + 2/3
Use Point-Slope form to find the equation.
m=3
(1,1)
y – y1 = m(x – x1)
y – 1 = 3(x – 1)
Write answer in Slope-Intercept Form.
y – 1 = 3x – 3
y = 3x – 2
Assignment
Worksheet
9-4b
& Pages
418-419
#’s 29-34,
41-46 All