Download 3.5: The Point-Slope Form of a Linear Equation

Intermediate Algebra
Finding Equations of Lines
Name _____________________________
Finding equations from graphs:
steps:
1. Find the y-intercept. (0, b)
2. Find the slope. m 
Ex 1:
Slope: down 1, right 1
m = -1
y-int: (0, 5), so b=5
Therefore,
rise
run
y  x  5
f ( x)   x  5
3. Plug into slope-intercept
formula y  mx  b .
Ex 2:
Slope: up 1, right 2
m=½
y-int: (0, 2), so b=2
Therefore,
1
x2
2
1
f ( x)  x  2
2
y
4. Put into function notation by
replacing y with f(x).
f ( x)  mx  b
You try: Find the equations of each line.
y
y
y
y
(0,6)
(0, 3)
(-3,0)
(10,0)
x
(-7,0)
_________________
x
x
x
(0,-4)
_________________
Finding Equations given a point and a slope:
steps:
1. Plug the point ( x1 , y1 ) and the slope, m, that
was given into the point-slope formula
y  y1  m( x  x1 ) .
2. Solve for y to get into slope intercept form:
y  mx  b .
3. Put into function notation by replacing y with f(x).
f ( x)  mx  b
_________________
__________________
Ex: Write an equation for a line with slope,
1
m  , and goes through the point (8, -2).
2
You try: Find the equation of each line.
3
,
5
2. Write an equation for the line with slope,
3
m   , and goes through the point (-8, 0).
4
3. Write an equation for the line with slope, m  0 ,
and goes through the point (5, -4).
4. Write an equation for the line with slope,
m  undefined , and goes through the point
(2, 7).
1. Write an equation for the line with slope, m 
and it goes through the point (-10, -2).
Finding Equations given 2 points:
steps:
y  y1
1. Calculate the slope. m  2
x2  x1
2. Use the slope, m, and choose either point to
plug into the point-slope formula
y  y1  m( x  x1 ) .
3. Solve for y to get into slope intercept form:
y  mx  b .
4. Put into function notation by replacing y with f(x).
f ( x)  mx  b
Ex: Write an equation for a line that goes
through the points (4, -3) and (-6, 2).
You Try: Find the equation of each line.
1. Write an equation for the line that goes through
the points (6, -2) and (-3, 4).
2. Write an equation for the line that goes through
the points (-7, -3) and (-6, -4).
3. Write an equation for the line that goes through
the points (-3, -2) and (-3, 4).
4. Write an equation for the line that goes through
the points (6, 4) and (-3, 4).
Finding Equations that Parallel or Perpendicular to Other Equations:
steps:
Ex: Write an equation for the line that goes
1. Put the equation given in slope intercept form
through the point (-6, 4) and perpendicular to
to determine the slope, m.
the graph of  2 x  3 y  9 .
2. Use the slope, m, to find the parallel or
perpendicular slope
 For parallel lines:
-use the same slope, m
 For perpendicular lines:
-use the negative reciprocal of m
3. Plug the point ( x1 , y1 ) and the parallel or
perpendicular slope, m, that was found in
step#2 into the point-slope formula
y  y1  m( x  x1 ) .
4. Solve for y to get into slope intercept form:
y  mx  b .
5. Put into function notation by replacing y with f(x).
f ( x)  mx  b
You Try: Find the equation of each line.
1. Write an equation for the line that goes
through the point (6, -1) and parallel to the
graph of 2 x  3 y  12 .
3. Write an equation for the line that goes
through the point (-4, 5) and perpendicular to
the graph of 3 y  15 .
5. Write an equation for the line that goes
through the point (2, 3) and parallel to the
line that goes through the points (2, 8) and
(4, 0).
2. Write an equation for the line that goes through
the point (-2, 2) and perpendicular to the graph of
4x  2 y  6 .
4. Write an equation for the line that goes through
the point (3, -7) and parallel to the graph of x  2 .
6. Write an equation for the line that goes
through the point (6, 9) and perpendicular to
the line that goes through the points (0, -2)
and (-5, 8).