# 2.4 Writing Equations of Lines

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```					   2.4 Writing
Equations of Lines
p. 91
• We’ve learned to graph
given an equation.
• Now we’ll learn to write the
equation given the graph
• There are three ways.
• It all depends on what
information you are given as
to which process you use.
Given the slope, m, and the y-
intercept, b, use the equation
y=mx+b
•The y-intercept is -3
•b=-3
3         •The slope is 4/3

4             •The equation is:
•y = 4/3x – 3
Use Point Slope Form:
If you are given slope, m, and a
point (x1,y1) on the line

•y – y1 = m ( x – x1)
Write an equation of a line
containing the point (1,2) with
slope of -1/2.

• Use (x1,y1) = (1,2) & m = -1/2

• y – 2 = -1/2 ( x – 1)
• Now you can simplify to the slope
intercept form
• y – 2 = -1/2 x + ½
• y = -1/2 x + 5/2
If you are given two points on the
line
• Find the slope using the two
points
• Then plug this slope and
either one of the points into
the point slope formula.
Given two points (-2,2) & (3,7)
• Find the slope:
• m=1
• Plug this slope and one of
the points into the point             (3,7)
slope formula.
(-2,2)
• y – 2 = 1 ( x – (-2))
• y–2=x+2
• y = x + 4 (put the
equation into slope
intercept form)
Direct Variation

• 2 variables X & Y show direct variation
provided   y = kx & k ≠ 0.
• The non-zero constant k is called the
constant of variation, & y is said to
vary directly with x.
• The graph of y=kx is a line thru the
origin.
The variables x & y vary directly,
& y = 12 when x = 4.
Write and graph an equation
relating x & y.
•   Use x & y to find the constant of variation
•   y = kx
•   12 = k4
•   3=k
•   The direct variation equation is y = 3x
•   This is what you MUST write as the
Graph y = 3x
In the same direct variation
equation, when x=5, find the
value of y.

• y = 3*5
• y = 15
Assignment

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