Title: 4'3 Linear Equations in two variables
14.3 Linear Equations in two variables
2In the previous sections we were asked to sketch
the line given its equation and find the slope of
a line. In this section we will find the equation
given certain information about the line.
3In order to do this there are 3 forms for
equations of lines with which we need to be
familiar. They are
- 1) standard form
- 2) slope-intercept form
- 3)point-slope form
4When writing the equation in standard form be
sure that A,B, and C have no fractions and that A
is positive. If A,B, or C are a fraction multiply
the equation by the LCD to remove fractions. If A
is negative then multiply both sides of the
equation by -1.
5Write each equation in standard form
6In order to write the equation for a line in
slope-intercept form, solve the equation for y.
Write each equation in slope-intercept form.
7To write the equation for a line
- Start with either the point-slope or
slope-intercept form - Substitute in the necessary information
- Finish by writing the equation in the specified
form
8To use the point-slope form we need a point the
line passes through and the slope of the
line.Write the standard form equation for the
line with slope -3 and going through the point
(-1,4)
9Use the point-slope form to write the equation
for the line through the points (5, 9) and (2,
-3). Write the line in slope-intercept form.
10Use the slope-intercept form to write the
standard form equation for the line with
slope-2/3 and b3
11Use the slope-intercept form to write the
standard form equation for the line that goes
through the points (-2,2) and (1, 6).
12Write each equation in slope-intercept form to
find the slope and the y-intercept then sketch
the graph.
13Tell whether the graphs of each pair of equations
are parallel, perpendicular, or neither.
14Write the equation of the line that passes
through the given point and is parallel to the
given line.
15Write the equation of the line that passes
through the given point and is perpendicular to
the given line