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Intermediate Algebra
Finding Equations of Lines
Name
Finding equations from graphs:
steps:
1. Find the ^/-intercept. (0, b)
Ex 1:
Slope: down 1, right 1
Ex 2:
Slope: up 1, right 2
m = -\
/W="/2
y-mi: (0, 5), so b=5
2. Find the slope, m = rise
run
Therefore,
\
'J
>'-int: (0, 2), so b=2
Therefore,
y--x + 5
f(x) = -x + 5
^ ^ ^ ^ ^
3. Plug into slope-intercept
formula _y = mx + b.
4. Put into function notation by
replacing;^ withy(;c).
/ ( x ) = mx + b
You try: Find the equations of each line.
(0.6-)
:
: (0,3)
(-3,0)
(10.0)
f-7.0)
m
(0.-4)
u
Finding Equations given a point and a slope:
steps:
1. Plug the point (JC, , >',) and the slope, m, that
was given into the point-slope formula
y-y^
=m(x-x^).
2. Solve for y to get into slope intercept form:
y = mx + b.
3. Put into function notation by replacing with/(x).
f(x)- mx + b
Ex: Write an equation for a line with slope,
/w =
, and goes through the point (8, -2).
You try: Find the equation of each Hne.
5'
2. Write an equation for the line with slope,
3
/w = - - , and goes through the point (-8,0).
3. Write an equation for the line with slope, m = 0,
and goes through the point (51^4).
>jv^
4. Write an equation for the line with slope,
m = undefined , and goes through the point
1. Write an equation for the line with slope, m =
and it goes through the point (-10, -2).
©7)
Finding Equations given 2 points:
steps:
Calculate the slope, m =
2. Use the slope, m, and choose either point to
plug into the point-slope formula
y-y^=m(x-x^).
3. Solve fory to get into slope intercept form:
y = mx + b.
4. Put into function notation by replacingy mthf{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).
2L
3. Write an equation for thejine that goes through
the points (d^-2) and
4).
=3=
4. Write an equation for theline that goes through
the points (6j@and (-3K4).
5
Finding Equations that Parallel or Perpendicular to Other Equations:
Ex: Write an equation for the line that goes
steps:
through the point (-6, 4) and perpendicular to
1. Put the equation given in slope intercept form
the graph of - 2.x - 33; = - 9 .
to determine the slope, m.
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
3. Plug the point (A:,,
and the parallel or
perpendicular slope, m, that was found in
step#2 into the point-slope formula
4. Solve for to get into slope intercept form:
y = mx + b.
5. Put into function notation by replacing y withj{x).
f(x) = mx + b
2.
= 2>
You Try: Find the equation of each Hne.
1. Write an equation for the Hne that goes
through the point (6,-1) and parallel to the
graph of 2x + 3y = 12 .
2. Write an equation for the line that goes through
the point (-2,%) and perpendicular to the graph of
4x-2y = 6.
-/k
3
U^-(-HV
-z -z-
-f(x-(o^
3. Write an equation for the line that goes
through the point @ 5) and perpendicular to
the graph of
- 15^
5. Write an equation for the line that goes
through the point (2, 3) and parallel to the
Hne that goes through the points (2, 8) and
(4,0).
>C^.O^.^
4. Write an e l a t i o n for the line that goes through
the point^/*-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).
>^2M^c
"2-/ so m jj ^
I
+3