Download MathMatters 3 Chapter 6 Lesson 6-3 Example 1 Write an equation of

MathMatters 3
Chapter 6
Lesson 6-3
Example 1
Write an equation of the line with slope of -3 and containing the point P(-3, 4).
Solution
y - y1
y-4
y-4
y-4
y
= m(x - x1)
= -3(x - (-3))
= -3(x + 3)
= -3x - 9
= -3x - 5
point-slope form
Substitute -3 for m, -3 for x1, and 4 for y1.
Solve for y.
slope-intercept form.
Example 2
Write an equation of the line that contains the points A(2, -3) and B(4, 3).
Solution
Given: x1 = 2, y1 = -3, x2 = 4, y2 = 3
y2 - y1 3 - (-3) 6
Find the slope of the line: m = x - x = 4 - 2 = 2 = 3
2
1
Find the equation using the point-slope form.
y - y1
y - (-3)
y+3
y
= m(x - x1)
= 3(x - 2)
= 3x - 6
= 3x - 9
Solve for y.
slope-intercept form
An equation of the line is y = 3x - 9.
MathMatters 3
Chapter 6
Example 3
PRODUCT DESIGN A technician is using a coordinate
grid to design a schematic for a circuit board. A connection
aligns with the line shown at the right. Write an equation of
the line.
Solution
y-intercepts:
slope:
The line intersects the y-axis at the point (0, 2).
The y-intercept is 2.
Use two points on the line whose coordinates are easily
determined.
Use (x1, y1) = (0, 2) and (x2, y2) = (3, -4).
-4 - 2 -6
m = 3 - 0 = 3 = -2
An equation of the line:
y = mx + b
y = -2x + 2
slope-intercept form
Example 4
2
Write an equation of a line parallel to y = x - 2 containing the point R(-2, 1).
3
Solution
2
y = 3x - 2
2
m=3
slope of line
2
Because parallel lines have equal slopes, m = 3.
y - y1 = m(x - x1)
2
y - 1 = 3(x - (-2))
2
4
y - 1 = 3x + 3
2
7
y = 3x + 3
point-slope form
x1 = -2, y1 = 1
2
7
An equation of the line is y = 3x + 3.