Section 3.4
Equations of a line
Nina Gurganus
Slope- Intercept Form
• Formula
Y= mx + b
Use on non-vertical lines only
Slope
Y-intercept
Example: Y= 4x + 2
Y= 4x + 2 represents the equation of a line with the slope of 4 and a yintercept of 2.
Point- Slope Form
• Point- Slope Form
y – y1 = m(x – x1)
Any point
Use on Non-vertical lines
Known point
Slope
You can get an equation of a line by using point slope form
Example: (2, 4) m=3
(y – 4)= 3 (x – 2)
Once you fill in the slope and points into the equation, solve.
Y – 4= 3x – 6
+4
+4
Y= 2x - 2
Two- Point
• y- y1
= y2 – y1
x- x1
x2 – x1
X and y are any two points on a line
X1, y1, x2, and y2 are known points
Can only be used on non- vertical lines
General Linear
• General Linear
• Equation= ax + by + c = 0
• A, b, and c are real numbers
• The equation can be used on any line
Intercept form
• Equation for intercept form:
x + y = 1
a
b
a is the x- intercept
b is the y- intercept
Use this formula with lines not passing through the origin
Horizontal Line
• Equation of a horizontal line:
y = b, where b is the y- coordinate of the y- intercept
Examples: If a horizontal like passes through the point (2, 5), then y
would equal 5.
B.
In this picture, y would = -2
Vertical Line
• Equation of a vertical line:
x = a, where a is the x- coordinate of every point on the line
Examples: If a vertical line passes through the points (2, -5), then X
would equal 2.
In the picture, since there is a line going through 1 on
the x axis, then x would = 1.
Standard
Form
• Equation
ax + by = c
a, b, and c are real numbers
A is greater than 0
And a , b , c are not fractions
Can be used on any line
Example: If the equation is y= 2x + 5, it would be changed to standard
form by changing it to 2x-y= -5
If you are left with a fraction in your equation, for example
y- 2= 2/3(x+2), you cannot have a fraction in your final answer, so
before solving the equation, you can multiply everything except for
what's in parenthesis by the denominator of the fraction, which in this
case would be 3. You would then be left with 3y-6= 2(x+2) which in
standard form would give you an equation of 2x- 3y=-10
Practice problems
1. Write an equation of a line that goes through the point (4, -2) and
has a slope of 2/3. (Write final answer in standard form)
2. Write an equation of a line that goes through the points (-2, 3) and
(6, 1). (Write answer in point- slope form)
3. Write an equation of a horizontal line that passes through points
(2, 4).
4. Write an equation of a vertical line that passes through points (1, 5).
5.Write an equation of a line that has a y- intercept of 4 and an xintercept of 1. (Write final answer in standard form).
Answers to practice problems
1. 2x – 3y = 14
2. Y – 1= -1/4 (X – 6)
3. Y = 4
4. X = 1
5. 4x + y = 4
Work to practice problems (#1-3)
1. (4, -2) m= 2/3
2. (-2, 3) (6, 1)
y + 2= 2/3 (x - 4)
3-1 = 2 = -1/4
(3) y + 2= 2/3 (x – 4) -2-6 -8
3y + 6= 2 (x – 4)
y – 1 = -1/4 (x – 6)
3y + 6= 2x – 8
3y + 14 = 2x
14= 2x – 3y
2x – 3y = 14
3. If a horizontal line
passes through points
(2,4), that means that it
would be passing
through the y axis at 4
which means that y=4.
Work to practice problems (#4,5)
4. If a vertical line passes through
5. (0,4) (1,0)
Points (1,5), that means that it would be 4-0 = 4 = -4
Passing through the x axis at point 1
0-1 -1
Meaning that x would = 1
Y- 4 = -4 (x – 0)
Y – 4 = -4x – 0
Y – 4 = -4x
4x + y = 4
Link to video
http://youtu.be/T4Ri8W46TpM
Work cited
• Section 3.4 packet
• "Classify Equations as Relations, Functions or One-to-one Functions."
Classify Equations as Functions, Relations or One to One Functions.
Practice Problems... N.p., n.d. Web. 14 Jan. 2016.