Tim charted his distance from home.
Plot the point (12, 18).
How many total minutes did Tim stop to rest?
How many times did Tim get closer to his home?
The speed from the 18th minute to the 20th minute is miles
per minute. (Remember that speed is never negative.)
To answer the questions about Tim's rest stops and getting closer to his home, we would need the full chart of Tim's distance from home. Without that information, we cannot determine the exact number of minutes Tim stopped to rest or how many times he got closer to his home.
Regarding the speed from the 18th to the 20th minute, we cannot determine it either since we don't know the corresponding distance covered during that time.
lot the point (12, 18).
POINT
SEGMENT
EDIT LABEL
UNDO
REDO
RESET
DELETE
Distance from home (in miles)
Minutes
0 24681012141618202468101214161820ABCDEFGHIJK
PLAY
STOP
I'm sorry, but as a text-based AI, I am unable to directly plot points or provide visual representations. However, I can provide you with a verbal description of the plotted point (12, 18).
The point (12, 18) means that at 12 minutes, Tim's distance from home was 18 miles.
Find the slope between the points
(
5
,
1
)
(5, 1) and
(
11
,
7
)
(11, 7) .
�
=
m=
To find the slope between the points (5, 1) and (11, 7), we can use the formula for slope, which is:
m = (y2 - y1) / (x2 - x1)
Plugging in the values, we get:
m = (7 - 1) / (11 - 5)
= 6 / 6
= 1
Therefore, the slope between the two points is 1.
Find the slope and y-intercept that has infinite solutions to the equation
−
6
�
+
3
�
=
42
−6x+3y=42
The slope would be
.
The y-intercept would be
. (Do not list as a coordinate point.)
To determine the slope and y-intercept of the equation -6x + 3y = 42, we need to rewrite it in slope-intercept form, which is y = mx + b, where m is the slope and b is the y-intercept.
-6x + 3y = 42
We rearrange the equation to isolate y:
3y = 6x + 42
Dividing both sides by 3:
y = 2x + 14
Now the equation is in slope-intercept form, y = mx + b, where the slope is 2 and the y-intercept is 14.
Solve the following inequalities.
5
�
<
30
5x<30
�
x
−
5
�
<
30
−5y<30
�
y
5
�
<
−
30
5z<−30
�
z
To solve the inequalities, we will treat them as regular equations and perform the same operation on both sides to maintain the inequality.
1) 5x < 30
Divide both sides by 5:
x < 6
2) -5y < 30
Divide both sides by -5 (Note that when you divide by a negative number, the inequality sign will flip):
y > -6
3) 5z < -30
Divide both sides by 5:
z < -6
Therefore, the solutions to these inequalities are:
1) x < 6
2) y > -6
3) z < -6
Find the slope and y-intercept that has infinite solutions to the equation
6
�
+
2
�
=
30
6x+2y=30
The slope would be
.
The y-intercept would be
. (Do not list as a coordinate point.)