Equations of Lines

Slopes of Lines:

slope	vertical rise	y - y
	horizontal run	x - x

Example:  Find slope of the coordinates: (8,-2) and (-4,5)
                                                          

-2-5	slope is	-7
8 - (-4)		12

Parallel Lines have same slope.
Ex. slope will still be -7/12

Perpendicular Lines have opposite slope.
(Flip fraction and change sign)
Ex. slope will be 12/7

Standard Form of a line is Ax + By = C

Slope-intercept Form of a line is y = mx + b
where m is the slope and b is the y-intercept.

Point Slope Form of a line is y - y₁ = m(x - x₁)
where m is the slope and x₁ and y₁ is the point.

Examples:

1. Write the equation of a line given slope is 5 and  y-intercept is -7. Since we have slope and y-int, we use slope-int form.              y = 5x - 7 is the equation.

2. Write the equation of a line given slope is ¾  and passes through (5,-3). Since we have slope and a point, we use point slope form. Then put in slope-int form by solving for y.             y -(-3) = ¾(x - 5)    Point slope form             y + 3 = ¾(x - 5)    distribute             y + 3 = ¾x - 3¾    subtract 3 from both sides                y = ¾x - 6¾        Slope-int form

3. Write slope-int form of a line that passes      through (-5,2) and (-7,3).     First, find slope -

2-3	slope is	-1
-5 - (-7)		2

Then use first point and slope with point slope form:               y - 2 = -½(x+5)                y - 2 = -½x-2½               y = -½x- ½

4. Write slope-int form of the line perpendicular to  y = 4x +9 and passes  (1,6).     First get perpendicular slope from     y = 4x + 9 - slope is 4 so perpendicular slope is -¼     Then write equation: y - 6 = -¼(x - 1)                                         y - 6 = -¼x + ¼                                            y = -¼x + 6¼

 

 

 

 

 

Example Problems Answers

1. Graph using x and y intercepts:  3x - 4y = 15

2. Graph using slope and y intercept:  y = -4x+2

3. Write slope intercept form of the line that has slope -2 and
    passes through (-5,3).

4. Write slope intercept form of the line that passes through
    (6,-2) and (5,4).

5. Write slope intercept form of the line parallel to y = 5x-3 and
    passes through (7,4).

6. Write slope intercept form of the line perpendicular to
    3x+4y=10 and passes through (3,-2).

7. Write slope intercept form of the line that has slope of -6 and
    has x intercept of 7.

8. Write slope intercept form of the line that passes through
    (-8,-3) and (-6,2).