Answer:
1. w = 15
2. b = 4.8
3. s = 9.7
4. p =15
5. m = -3.2
Step-by-step explanation:
1.w + 10 = 25
we have to find the value of w, so moving 10 from left side to right side
w= 25 - 10
w = 15
2. 7.2 + b = 12
we have to find the value of w, so moving 7.2 from left side to right side
b= 12 - 7.2
b= 4.8
3. 5.3 + s = 15
s= 15 - 5.3
s= 9.7
4.p + (-25) = -10
p-25 = -10
p= -10 + 25
p= 15
3. m + (-1.6) = -4.8
m - 1.6 = -4.8
m = -4.8 + 1.6
m= -3.2
Answer: y
=
−
2
3
x
+
2
Explanation:
Given that we have the slope and a point on the graph we can use the point slope formula to find the equation of the line.
Point-Slope Formula:
y
−
y
1
=
m
(
x
−
x
1
)
, where
m
is the slope of the line and
x
1
and
y
1
are x and y coordinates of a given point.
We can summarize the information already given:
m
=
−
2
3
x
1
=
6
y
1
=
−
2
Using this information, we can substitute these values onto the point-slope formula:
y
−
(
−
2
)
=
−
2
3
(
x
−
(
6
)
)
y
+
2
=
−
2
3
(
x
−
6
)
The equation above is the equation of the line in point-slope form. If we wanted to have the equation in
y
=
m
x
+
b
form then we simply solve the equation above for
y
y
+
2
=
−
2
3
x
+
12
3
y
+
2
−
2
=
−
2
3
x
+
12
3
−
2
y
=
−
2
3
x
+
12
3
−
2
(
3
3
)
y
=
−
2
3
x
+
12
3
−
6
3
y
=
−
2
3
x
+
6
3
y
=
−
2
3
x
+
2y
=
−
2
3
x
+
2
Explanation:
Given that we have the slope and a point on the graph we can use the point slope formula to find the equation of the line.
Point-Slope Formula:
y
−
y
1
=
m
(
x
−
x
1
)
, where
m
is the slope of the line and
x
1
and
y
1
are x and y coordinates of a given point.
We can summarize the information already given:
m
=
−
2
3
x
1
=
6
y
1
=
−
2
Using this information, we can substitute these values onto the point-slope formula:
y
−
(
−
2
)
=
−
2
3
(
x
−
(
6
)
)
y
+
2
=
−
2
3
(
x
−
6
)
The equation above is the equation of the line in point-slope form. If we wanted to have the equation in
y
=
m
x
+
b
form then we simply solve the equation above for
y
y
+
2
=
−
2
3
x
+
12
3
y
+
2
−
2
=
−
2
3
x
+
12
3
−
2
y
=
−
2
3
x
+
12
3
−
2
(
3
3
)
y
=
−
2
3
x
+
12
3
−
6
3
y
=
−
2
3
x
+
6
3
y
=
−
2
3
x
+
2
Step-by-step explanation:
The given linear system is:
The question is asking to solve using elimination. When eliminating, you can either eliminate x or y. In this system, y is much easier to eliminate. The y variable in both equations are 7y. To eliminate, one of them has to be negative, so multiply one of the equations by -1.
I will be multiplying the second equation by -1.
Rewrite the system:
Subtract:
Lastly, you need to leave the variable x alone. The variable is currently -6x or -6 times x. To remove it, you need to do the opposite of it, which is dividing by -6.
Now that you have the value of x, substitute it into one of the equations to find y. I will be substituting it into the first equation.
Open the parentheses and multiply:
Move 5 to the other side to leave the variable alone:
You will be subtracting since you're "removing" it by doing the opposite of it.
Lastly, divide both sides by 7 to leave y alone.
The answer is (1, 4).
