Transcript Lines in the Coordinate Plane LESSON 3-6 Additional Examples Use the slope and y-intercept to graph the line y = –2x + 9. When.

Lines in the Coordinate Plane
LESSON 3-6
Additional Examples
Use the slope and y-intercept to graph the line y = –2x + 9.
When an equation is written in the form y = mx + b, m is the slope
and b is the y-intercept.
In the equation y = –2x + 9, the slope is –2 and the y-intercept is 9.
Quick Check
HELP
GEOMETRY
Lines in the Coordinate Plane
LESSON 3-6
Additional Examples
Use the x-intercept and y-intercept to graph 5x – 6y = 30.
To find the x-intercept, substitute
0 for y and solve for x.
To find the y-intercept, substitute
0 for x and solve for y.
5x – 6y = 30
5x – 6(0) = 30
5x – 0 = 30
5x = 30
x =6
5x – 6y = 30
5(0) – 6y = 30
0 – 6y = 30
–6y = 30
y = –5
The x-intercept is 6.
A point on the line is (6, 0).
The y-intercept is –5.
A point on the line is (0, –5).
HELP
GEOMETRY
Lines in the Coordinate Plane
LESSON 3-6
Additional Examples
(continued)
Plot (6, 0) and (0, –5). Draw the line containing the two points.
Quick Check
HELP
GEOMETRY
Lines in the Coordinate Plane
LESSON 3-6
Additional Examples
Transform the equation –6x + 3y = 12 to slope-intercept form,
then graph the resulting equation.
Step 1: Transform the equation
to slope-intercept form.
–6x + 3y = 12
3y = 6x + 12
3y
6x
12
=
+
3
3
3
Step 2: Use the y-intercept and
the slope to plot two points
and draw the line containing them.
Add 6x to each side.
Divide each side by 3.
y = 2x + 4
The y-intercept is 4 and the slope is 2.
Quick Check
HELP
GEOMETRY
Lines in the Coordinate Plane
LESSON 3-6
Additional Examples
Write an equation in point-slope form of the line with slope –8
that contains P(3, –6).
y – y1 = m(x – x1)
y – (–6) = –8(x – 3)
y + 6 = –8(x – 3)
Use point-slope form.
Substitute –8 for m and (3, –6) for (x1, y1).
Simplify.
Quick Check
HELP
GEOMETRY
Lines in the Coordinate Plane
LESSON 3-6
Additional Examples
Write an equation in point-slope form of the line that contains
the points G(4, –9) and H(–1, 1).
Step 1: Find the slope.
y –y
m = x2 – x1
2
1
Use the formula for slope.
1 – (–9)
m = –1 – 4
Substitute (4, –9) for (x1, y1) and (–1, 1) for (x2, y2).
10
m = –5
m = –2
HELP
Simplify.
GEOMETRY
Lines in the Coordinate Plane
LESSON 3-6
Additional Examples
(continued)
Step 2: Select one of the points.
Write the equation in point-slope form.
y – y1 = m(x – x1)
y – (–9) = –2(x – 4)
y + 9 = –2(x – 4)
Point-slope form
Substitute –2 for m and (4, –9) for (x1, y1).
Simplify.
Quick Check
HELP
GEOMETRY
Lines in the Coordinate Plane
LESSON 3-6
Additional Examples
Write equations for the horizontal line and the vertical line that
contain A(–7, –5).
Every point on the horizontal line through A(–7, –5)
has the same y-coordinate, –5, as point A.
The equation of the line is y = –5.
It crosses the y-axis at (0, –5).
Every point on the vertical line through A(–7, –5)
has the same x-coordinate, –7, as point A.
The equation of the line is x = –7.
It crosses the x-axis at (–7, 0).
HELP
Quick Check
GEOMETRY