3.3 Equation of a Line 1310 Fall 2011
Straight Line Formats
Slope Intercept form: y = mx + b
Point Slope form: ( y - y1 ) = m ( x - x1 )
Remember definition of slope m 
y2  y1
x2  x1
General Form: Ax + By = C
Use Slope and Intercept to Write the Equation of a Line
If you have the slope, m, and the y-intercept, (0, b), write the equation as y = mx + b
[08] For a line with a slope of 3 and a y-intercept of (0,3), write the equation in slope intercept format.
Use Point-Slope Form to Write the Equation of a Line
If you are given a point on the line, (x1, y1), and the slope, m, substitute the values in the Point-Slope Form and
simplify.
y – y1 = m ( x – x1 )
[22] Given a slope of 3 and a point (3,-5), write the equation in Slope-Intercept form.
To write the equation in Standard format, write the equation in any (normally Slope-Intercept) form, then
put the variables on left side and the constant on right side.
[36] Given the points, (3,-4) and (-1,9), write the equation in Slope-Intercept and Standard Form.
Write an Equation of a Line Parallel to a Given Line
Two lines are parallel if they have the same slope.
Note: If the slopes are equal and y-intercepts (0,b) are also equal, both lines are the same
To write an equation of a line parallel to a given line going through a specific point, determine slope of given
line, then substitute the values in the Point-Slope form.
[60] Write the equation parallel to y = 2x – 5 going thru ( -5, -7 ).
Write an Equation of a Line Perpendicular to a Given Line
Two lines are perpendicular if the slope of the second is the negative reciprocal of the first. (flip-flop, change
sign)
Examples: 3 and -1/3 ; -2/5 and 5/2
To write an equation of a line perpendicular to a given line going through a specific point, determine
slope of given line, flip-flop, change sign of slope then substitute the values in the Point-Slope
form.
[68] Write the equation perpendicular to y = ½ x – 7 going through ( -1, 5 ).
Extra Exercises
Are the following parallel, perpendicular, neither
[46] y = (2/5) x – 2;
y = (2/5) x + 2
[48] y = (-2/5) x + 4; y = (5/2) x – 6
[50] y = (-1/4) x + 5; y = -4x
[xx] y = 5;
x = -2