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•The slope is 4/3

•The equation is:•y = 4/3x – 3

4

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 slope formula.

• y – 2 = 1 ( x – (-2))• y – 2 = x + 2• y = x + 4 (put the

equation into slope intercept form)

(-2,2)

(3,7)

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

answer!

Graph y = 3x

In the same direct variation equation, when x=5, find the

value of y.

•y = 3*5

•y = 15

Assignment