1. 2.4 Writing Equations of Lines

2. In this lesson you will:
Write linear equations.
Write direct variation equations.

3. Writing an Equation of a Line
You can write the equation of a line using one of the following handy-dandy formulas:
Slope-Intercept form: (Given the slope m and the y-intercept b) use this equation):
Point-Slope Form: (Given the slope m and a point (x1,y1), use this equation):
In calculus we consider this formula to be one of our “best friends.”
Two Points: (Given two points (x1,y1) and (x2,y2), use the equation)
Use this formula to find the slope m, then use the point-slope form with this slope and either of the given points to write an equation of the line.

4. Write the equation of the line shown:
The y – intercept is -2
The slope is 3/2
y = (3/2)x-2

5. And finally simplify to y = (-1/2)x+4
Write the equation of the line that passes through (2,3) and has slope -1/2.
Use the point-slope formula:
y-3=(-1/2)(x-2)
And finally simplify to y = (-1/2)x+4

6. Write the equation of the line that passes through (3,2) and is a) perpendicular and b) parallel to y = -3x + 2.
The parallel line will have slope -3 and the perpendicular line will have slope 1/3.
Perpendicular
Parallel
y=(1/3)x+1
y-2=-3(x-3)
y = -3x+11
y-2=(1/3)(x-3)

7. Write the equation of the line that passes through (-2,-1) and (3,4)
First determine the slope:
You now know the slope and can use either of the given points in the point-slope formula.
Would you get the same answer if you used either given point?
y = x + 3

8. Two variables show direct variation provided y=kx and k is not 0.
K is called the constant of variation and y is said to vary directly with x. The graph of y = kx is a line through the origin.
The variables x and y at the right vary directly, and y=12 when x=4.
Write an equation relating x and y.
Find y when x is 5.
(5,15)
(4,12)
Note: In direct variation the ratio y/x is constant.

9. Does the data show a direct variation between x and y?
This data shows information about 14-karat Gold Chains (1 gram per inch)
Length, x (inches) 16 18 20 24 30
Price, y (dollars)
288
324
360
432
540
Does the data show a direct variation between x and y?
To decide if there is a direct variation, check whether the quotient of y and x is constant.
Yes, the data shows direct variation and the direct variation equation is y = 18x.

10. Does the data show direct variation?
Loose Diamonds (round, colorless, very small flaws)
Weight, x (carats)
0.5
0.7
1.0
1.5
2.0
Price, y (dollars)
2250
3430
6400
11,000
20,400
Does the data show direct variation?

11. Homework odd, 59, 63