1. 2.4 Writing Equations of Lines

2. In this lesson you will:
Write linear 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