Warm Up! – Graph the line that
satisfies each condition
1) Slope = -4, passes
2) Contains A(-1, -3), parallel
3) Contains M(4, 1),
passes through
to line CD with C(-1, 6) and
to line GH with G(0, 3)
P (-2, 1)
D(4, 1)
and H(-3, 0)
Slope of line CD is -1, so
Slope of line GH is -1, so
slope of || line is also -1.
slope of
line is 1.
Equations of Lines
Section 3-4
Writing Equations of
Lines
• Remember from Algebra that an equation of
a line can be written given any of the
following:
– The slope and y-intercept (slope-intercept form)
– The slope and the coordinates of a point on the
line (point-slope form) or,
– The coordinates of two points on the line
Example 1 – Writing an equation of a
line given slope and the y-intercept
“Write an equation in slope-intercept form of the line with
slope of -3 and y-intercept of 2.”
y = mx + b
y = -3x + 2
Example 2 – Writing an equation of a
line given slope and a point on the line.
“Write an equation in point-slope form of the line with
slope of ½ that contains (1, -4).”
y – y1 = m(x – x1)
y + 4 = ½ (x – 1)
Example 3 – Writing an equation of a line
given two points on the line.
“Write an equation of the line that passes through (-1, 0)
and (1, 2).”
y – y1 = m(x – x1)
y – 0 = 1(x - -1)
y=x+1
Try these examples on your own
1.) Write the equation of the line in slope-intercept form that has a slope of ½ and
y-intercept of -4.
2.) Write the equation of the line in point-slope form that has a slope of -2 and
passes through point (3, -4).
3.) Write the equation of the line AB in slope-intercept form where A(-4, 0) and
B(2, -3).
Example 4 – Writing Equations of
Parallel Lines
“Write the equation of the line that passes through (1, 3) and is
parallel to the line y = -2x + 3”
y – y1 = m(x – x1)
y = -2x + 5
Answer left in slope-intercept form
Example 5 – Writing Equations of
Perpendicular Lines
“Write the equation of the line that passes through (-4, 2) and
is perpendicular to the line y = ¼x + 3”
y – y1 = m(x – x1)
y = -4x - 14
Answer left in slope-intercept form
Try these examples on your own
1.) Write an equation of the line that passes through K(5, 0) and is parallel to line
AB where A(0, 2) and B(-4, 3).
2.) Write an equation of the line that passes through Z(-1, -3) and is perpendicular
to line CD where C(1, 2) and D(4, 0).