Aim #21: How do we write and graph lines in point-slope form?
Homework: Handout
Do Now: a) On the graph provided, plot (3, 4)
and draw a line through this point
if the slope is 2.
b) Write the equation of this line.
10-20-16
c) What do you know about the
slope between any two points on this line?
Since the slope is the same between any two points on a given line, it is possible to
write the equation of a line knowing only one point and the slope.
Consider the slope formula:
m=
y2 - y1
x2 - x1
Let (x1, y1) be a given point on a line whose slope is m and let (x, y) be any other
point on the line.
With this information we can now rewrite the slope formula as:
m=
y - y1
x - x1
Now, by cross multiplying, we get:
y - y1 = m(x - x1)
which is the point-slope form of the equation of a nonvertical line that passes
through the point (x1, y1) and has slope m.
1) a) Write the equation of the line that passes through the point (3, 4) and has
a slope of 2 in point-slope form.
b) Rewrite your answer from part a in slope-intercept form showing this is the
same line found in the Do Now.
Homework #20 Solutions: Pg 115 #1 - 9, 12 - 13, 16 - 21
Pg 120 #2 - 20 even
Pg 120 #2 - 20 even
2) Write an equation in point-slope form for the line through the given point that
has the given slope.
a) (3, -4); m = 6
b) (4, 2); m =
c) (5, 0); m = 1
d) (1, -8); m =
e) (-4, 7); m = -2
f) (6, -5); m =
3) Write an equation in point-slope form for the line that passes through the two
given points.
a) (2, 7), (1, -4)
b) (3, 5), (0, 0)
c) (-1, -5), (-7, -6)
d) (7, -3), (-1, 1)
e) (4, 8), (8, 11)
f) (-8, 0), (1, 5)
4) Write an equation for the line that passes through (3, -5) and (-2, 1) in
point-slope form and slope-intercept form.
5) For each equation given in point-slope form, state the point and the slope of
the line represented in the equation.
a) y - 5 =
(x + 9)
b) -(x - 2) = y - 10
6) Graph each equation.
a) y + 4 = 3(x - 2)
b) y - 1 =
(x - 6)
c) y - 8 = -4(x + 2)
d) y + 3 =
(x + 5)
Sum it up!
Another way to represent the equation of a line, besides slope-intercept form, is
point-slope form which identifies both a point on the line and the slope of the
line.