2.3 Quick Graphs of Linear Equations and 2.4 Writing Equations of Lines
The SLOPE INTERCEPT form of a line is y = mx + b
STANDARD FORM OF A LINE:
Ax + By = C where A, B, and C are integers and A > 0
y = −2x + 3
y=
2
x−3
3
2
1
y=− x+
5
2
x-intercept: __________________
x-intercept: __________________
x-intercept: __________________
Standard Form:_______________
Standard Form:_______________
Standard Form:_______________
What formula can you use to generalize the slope of a line if the equation is given in standard form ?
m = ______
5x + 3y = -15
slope:______
y-intercept:___________
y = 3x
x-intercept: __________________
x-intercept:_______
y=7
x-intercept: __________________
x = −4
x-intercept: __________________
2.3 Quick Graphs of Linear Equations and 2.4 Writing Equations of Lines
Graph then write an equation of the line that passes through the point ( -3, 4) and m =
1.) Slope-Intercept Form: y = mx + b
2.) Point-Slope Form: y − y1 = m( x − x1 )
3.) Standard Form: Ax + By = C
4.) Given Two Points: Write the equation of the line that passes through (−2,−1) and (3,4)
5.) Write the equation of the line shown. State your answer in slope-intercept Form.
2
3
2.3 Quick Graphs of Linear Equations and 2.4 Writing Equations of Lines
Writing Equations of Parallel and Perpendicular Lines.
Parallel Lines: Two lines are parallel if and only if they have the same ___________.
Perpendicular lines: Two lines are perpendicular if and only if their slopes are
___________________________
__________________ of each other.
Key Questions:
All types of vertical lines are parallel to what types of lines? _______________________
All types of vertical lines are perpendicular to what types of lines? _________________
Graph and use the slope formula tell whether the lines are parallel, perpendicular or neither.
Line 1: through (−3,3) and (3,−1)
Line 2: through (−2,−3) and (2,3)
Write an equation of the line that passes through ( 2, -3) and is parallel to the line that
passes through (3, 5) and (-1, -3)
Write an equation of the line that passes through ( 3, 2) and is perpendicular to the line
y = −3 x + 2
Write an equation of a line that passes through ( 3, -5) that is
a.) perpendicular
b.) parallel
to the line x = 4.
2.3 Quick Graphs of Linear Equations and 2.4 Writing Equations of Lines