Download Do Now 11/28/06

Do Now 11/28/11
In your notebook, explain if the equations below are the
same line.
y – 5 = 3(x + 2)
y = 3x + 11
y – 3 = 2(x – 1)
y = 2x + 1
y – 2 = 3(x + 5)
y = 3x + 17
y + 3 = 2(x + 2)
y = 2x + 1
No
Yes
Objective
5.4 write linear equations in standard
form.
Section 5.4 “Write Linear
Equations in Standard Form”
The STANDARD FORM of a linear
equation is represented as
Ax + By = C
where A, B, and C are real numbers
Write two equations in standard form that
are equivalent to 2x – 6y = 4.
SOLUTION
To write one equivalent
equation, multiply each
side by 2.
4x – 12y = 8
To write another equivalent
equation, multiply each side
by 0.5.
x – 3y = 2
Write an equation in standard form of the line shown.
STEP 1
Calculate the slope.
m=
1 – (–2)
3
= –1 = – 3
1 –2
STEP 2
Write an equation in point-slope form. Use (1, 1).
y – y1 = m(x – x1)
y – 1 = – 3(x – 1)
STEP 3
Write point-slope form.
Substitute 1 for y1, -3 for m
and 1 for x1.
Rewrite the equation in standard form.
3x + y = 4
Simplify. Collect variable terms on
one side, constants on the other.
Write an equation in standard form of the line that
passes through the points (3, -1) and (2, -3).
STEP 1
Calculate the slope.
m=
-3 – (–1)
-2
= -1 = 2
2 –3
STEP 2
Write an equation in point-slope form. Use (3, -1).
y – y1 = m(x – x1)
y + 1 = 2(x – 3)
Write point-slope form.
Substitute 3 for x1, –1 for y1
and 2 for m.
STEP 3
Rewrite the equation in standard form.
-2x + y = -7
Simplify. Collect variable terms on
one side, constants on the other.
Write an equation of the specified line.
a.
Blue line
b.
Red line
SOLUTION
a.
The y-coordinate of the given point on the blue
line is –4. This means that all points on the line
have a y-coordinate of –4. An equation of the
line is y = –4.
b.
The x-coordinate of the given point on the red
line is 4. This means that all points on the line
have an x-coordinate of 4. An equation of the
line is x = 4.
Write an equation of the horizontal and vertical lines
that pass through the given point. (13, –5)
SOLUTION
STEP 1
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.
STEP 2
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.
Complete an equation in standard form
Find the missing coefficient in the equation of the line
shown. Write the completed equation.
SOLUTION
STEP 1
Find the value of A. Substitute the coordinates
of the given point for x and y in the equation.
Solve for A.
Write equation.
Ax + 3y = 2
Substitute – 1 for x and 0 for y.
A(–1) + 3(0) = 2
Simplify.
–A = 2
A = – 2 Divide by – 1.
STEP 2
Complete the equation.
– 2x + 3y = 2
Substitute – 2 for A.
Find the missing coefficient in the equation of the line
that passes through the given point. Write the
completed equation. Ax + y = –3, (2, 11)
STEP 1
Find the value of A. Substitute the coordinates
of the given point for x and y in the equation.
Solve for A.
Write equation.
Ax + y = -3
Substitute 2 for x and 11 for y.
A(2) + (11) = -3
Simplify.
2A = -14
Divide by 2.
A = –7
STEP 2
Complete the equation.
– 7x +y = –3
Substitute –7 for A.