#1
Decide whether or not the following equation has a circle as its graph. If it does, give the
center and the radius. If it does not, describe the graph.
X^2+y^2-12x+10y=-25
Yes, it does graph as a circle.
The center is at (6, -5)
The radius is 6.
#2
Let f(x)=-3x+4 and g(x)=-x^2+4x+1. Find and simply
(a) f(-3) (b)f(3t-2)
a) f(-3) = -3(-3) + 4 = 9 + 4 = 12
b) f(3t – 2) = -3(3t – 2) + 4 = -9t + 6 + 4 = -9t + 10
#3
Graph the following linear function. Identify any constant functions. Give the domain and
range.
F(x)=3
The graph of f(x) = 3 looks like this:
#4
Find the slope of the line satisfying the given condition: through (5,-3) and (1,-7)
m=
−7 − (−3) −7 + 3 −4
=
=
=1
1− 5
−4
−4
#5
Graph the line passing through the given point and having the indicated slope. Plot two
points on the line.
(a) through (-2,8), m=-1
The equation of the line will have the form y = -x + b, since the slope is -1.
Substitute the given point and solve for b:
8 = -(-2) + b
8=2+b
b=8–2
b=6
The equation of the line is y = -x + 6
The graph of the line looks like this:
(b) through (9/4, 2), undefined slope
A line with undefined slope is a vertical line. In other words, the x-value is
constant and only the y value varies.
In this case, the equation of that line is x = 9/4
The graph of this line looks like this:
#6
Write an equation for the following lines described and give the answers in a standard
form:
(a) Through ( 2, 4), m=-1
Using the slope, write the equation as y = -1x + b
Substitute the given point and solve for b:
4 = -(2) + b
4+2=b
b=6
y = -x + 6
Rearranging this into standard form gives:
x+y=6
(b) Through (-4,3), m=3/4
Write this in y = mx + b form:
y = (3/4)x + b
Substitute the given point and solve for b:
3 = (3/4)(-4) + b
3 = -3 + b
b=3+3
b=6
y = (3/4)x + 6
4y = 3x + 24
-3x + 4y = 24
(c) Through (5,1), undefined slope
As mentioned above, an undefined slope corresponds to a vertical line.
For this, since the x value is constant, the equation of the vertical line through
the point (5, 1) is:
x=5
#7
Give the slope and Y-intercept of the following line and graph it:
4x-y=7
Rewrite the equation as y = 4x – 7.
The slope is 4.
The y-intercept is (0, -7)
The graph of the equation looks like this:
#8
Write an equation (a) in standard form (b) in slope-intercept form for the lines described
(1) Through (3, -2), parallel to 2x-y=5
Rewrite the given equation in y = mx + b form:
y = 2x – 5
The slope of this line is 2.
The slope of a line parallel to this will also have a slope of 2.
The equation of the parallel line will have the form y = 2x + b
Substitute the given point and solve for b:
-2 = 2(3) + b
-2 = 6 + b
b = -2 – 6
b = -8
The equation of the parallel line is then y = 2x – 8
(2) Through (4, -4), perpendicular to x=4
The line x = 4 is a vertical line, with an undefined slope.
A line perpendicular to this will be a horizontal line, with a slope of 0.
The horizontal line through the point (4, -4) is y = -4.
#9
Determine whether the three points are collinear by using slopes. (0,-7), (-3,5),(2, -15)
The slope between the first and second points is:
m=
5 − (−7) 5 + 7 12
=
=
= −4
−3− 0
−3 −3
The slope between the first and third points is:
m=
−15 − (−7) −15 + 7 −8
=
=
= −4
2−0
2
2
The slope between the second and third points is:
m=
−15 − 5 −20 −20
=
=
= −4
2 − (−3) 2 + 3
5
Since all three slopes are equal, the three points are collinear.