2.4 Writing Equations of Lines p. 91

Learning Target I can write equations of a line.

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 (x 1,y 1 ) on the line y – y 1 = m ( x – x 1 )

Write an equation of a line containing the point (1,2) with slope of -1/2. Use (x 1,y 1 ) = (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

Resources epartments/MathDept/spitz/Cour ses/Algebra2/presentations.htm