Download Aim #21 - Manhasset Public Schools

Homework #20 Solutions: Pg 115 #1 - 9, 12 - 13, 16 - 21
Pg 120 #2 - 20 even
Pg 120 #2 - 20 even
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.
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.
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.