the slope is m= = –^86 = –^43 .Now,we
equate the expression obtained by computing
the slope of this line using the points (–3,–1)
and (0,y) to –^43 , and solve for y:= –^43 = –^43
y+ 1 = –4
y= –5Set 17 (Page 31)
- d.The points on the line y= –3 are of the form
(x,–3), for all real numbers x. This set of points
forms a horizontal line containing the point
(0,–3). The correct graph is given by choice d. - b.The slope of this line segment is m=
= –^53 . - b.The y-axis is a vertical line and hence, its
slope is undefined. - d.The slope of this line segment is
m= = 182 = ^23 . - c.The slope is 2 (so that the graph of the line
rises from left to right at a rate of two vertical
units up per one horizontal unit right) and the
y-intercept is (0,3). The correct graph is shown
in choice c. - a.The slope is –2 (so that the graph of the line
falls from left to right at the rate of two vertical
units down per one horizontal unit right) and
the y-intercept is (0,9). The correct graph is
shown in choice a. - d.The slope is –^52 (so that the graph of the line
falls from left to right at a rate of five vertical
units down per two horizontal units right) and
the y-intercept is (0,–5). The correct graph is
in choice d.
264. d.The line falls from left to right at a rate of
one vertical unit down per one horizontal unit
right, and it crosses the y-axis at the point
(0,7). So, the slope of the line is –1 and its
y-intercept is (0,7). Its equation is therefore
y= –x+ 7.
265. b.Using the two points (0,5) and (–9,–1) on
the line, we observe that the line rises from left
to right at a rate of six vertical units up per
nine horizontal units right. Hence, its slope is
^69 = ^23 . Also, it crosses the y-axis at (0,5). Thus,
the equation of this line is y= ^23 x+ 5.
266. c.First, convert the equation ^23 y– ^12 x= 0 into
slope-intercept form:
^23 y– ^12 x= 0
^23 y= ^12 xy= ^32 ^12 x= ^34 x
From this, we observe that since the slope is ^34 ,
the graph of the line rises from left to right at a
rate of 3 vertical units up per 4 horizontal units
right. The y-intercept is the origin, and the
correct graph is shown in choice c.- b.A line with a positive slope rises from left to
right. The only line that rises from left to right
is the one in choice b. - a.A line with an undefined slope must be ver-
tical. The only graph that satisfies this criterion
is choice a. - d.First, convert the equation into slope-intercept
form as follows:
0.1x– 0.7y= 1.4
0.1x= 0.7y+ 1.4
0.1x– 1.4 = 0.7y
y= ^00 .. 71 x– ^10 ..^47 = ^17 x– 22 –(–6)
10 –(–2)0 – (–5)
–3 – 0y+ 1
3y– (–1)
0 – (–3)(–1) – (–9)
(–3) –3ANSWERS & EXPLANATIONS–