Transcript ppt 4-3 Writing Equations in Point

Over Lesson 4–2
Over Lesson 4–2
Writing Equations in
Point-Slope Form
Lesson 4-3
You wrote linear equations given either one
point and the slope or two points.
• Write equations of lines in point-slope form.
• Write linear equations in different forms.
Write and Graph an Equation in Point-Slope Form
Write the point-slope form of an equation for a line
that passes through (–2, 0) with slope
Point-slope form
(x1, y1) = (–2, 0)
Simplify.
Answer:
Write and Graph an Equation in Point-Slope Form
Graph the equation
Plot the point at (–2, 0).
Use the slope to find another point on the line. Draw a
line through the two points.
Answer:
Write the point-slope form of an
equation for a line that passes
through (4, –3) with a slope of –2.
A. y – 4 = –2(x + 3)
B. y + 3 = –2(x – 4)
C. y – 3 = –2(x – 4)
D. y + 4 = –2(x – 3)
Writing an Equation in Standard Form
In standard form, the variables are on the left side of
the equation. A, B, and C are all integers.
Original equation
Multiply each side by 4 to
eliminate the fraction.
Distributive Property
Writing an Equation in Standard Form
4y – 3x = 3x – 20 – 3x
–3x + 4y = –20
3x – 4y = 20
Subtract 3x from each side.
Simplify.
Multiply each side by –1.
Answer: The standard form of the equation is
3x – 4y = 20.
Write y – 3 = 2(x + 4) in standard form.
A. –2x + y = 5
B. –2x + y = 11
C. 2x – y = –11
D. 2x + y = 11
Writing an Equation in Slope-Intercept Form
Original equation
Distributive Property
Add 5 to each side.
Writing an Equation in Slope-Intercept Form
Simplify.
Answer: The slope-intercept form of the equation is
Write 3x + 2y = 6 in slope-intercept form.
A.
B. y = –3x + 6
C. y = –3x + 3
D. y = 2x + 3
Point-Slope Form and Standard Form
A. GEOMETRY The figure shows trapezoid ABCD
with bases AB and CD.
Write an equation in___
point-slope form for the line
containing the side BC.
Point-Slope Form and Standard Form
Step 1 Find the slope of BC.
Slope formula
(x1, y1) = (4, 3) and
(x2, y2) = (6, –2)
Point-Slope Form and Standard Form
Step 2 You can use either point for (x1, y1) in the
point-slope form.
Using (4, 3)
Using (6, –2)
y – y1 = m(x – x1)
y – y1 = m(x – x1)
Point-Slope Form and Standard Form
B. Write an equation in standard form for the same
line.
Original equation
Distributive Property
Add 3 to each side.
2y = –5x + 26
5x + 2y = 26
Answer: 5x + 2y = 26
Multiply each side by 2.
Add 5x to each side.
A. The figure shows right triangle
ABC. Write the point-slope form of
the line containing the
hypotenuse AB.
A. y – 6 = 1(x – 4)
B. y – 1 = 1(x + 3)
C. y + 4 = 1(x + 6)
D. y – 4 = 1(x – 6)
B. The figure shows right triangle
ABC. Write the equation in standard
form of the line containing the
hypotenuse.
A. –x + y = 10
B. –x + y = 3
C. –x + y = –2
D. x – y = 2
Homework
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