What is the equation of the line that is parallel to y=x+4 and that passes through (5,–4)?
1 answer:
Answer:
y = x - 5
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
y = x + 4 ← is in slope- intercept form
with slope m =
• Parallel lines have equal slopes , then
y = x + c ← is the partial equation
to find c substitute (5, - 4 ) into the partial equation
- 4 = 1 + c ⇒ c = - 4 - 1 = - 5
y = x - 5 ← equation of parallel line
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The <u>correct answer</u> is:
D)
.
Explanation:
We solve each system to find the correct answer.
<u>For A:</u>
Since we have the coefficients of both variables the same, we will use <u>elimination </u>to solve this.
Since the coefficients of y are -2 and 2, we can add the equations to solve, since -2+2=0 and cancels the y variable:
Next we divide both sides by 6:
6x/6 = 23/6
x = 23/6
This is <u>not the x-coordinate</u> of the answer we are looking for, so <u>A is not correct</u>.
<u>For B</u>:
For this equation, it will be easier to isolate a variable and use <u>substitution</u>, since the coefficient of both x and y in the first equation is 1:
x-y=-2
Add y to both sides:
x-y+y=-2+y
x=-2+y
We now substitute this in place of x in the second equation:
4x-3y=11
4(-2+y)-3y=11
Using the distributive property, we have:
4(-2)+4(y)-3y=11
-8+4y-3y=11
Combining like terms, we have:
-8+y=11
Add 8 to each side:
-8+y+8=11+8
y=19
This is <u>not the y-coordinate</u> of the answer we're looking for, so <u>B is not correct</u>.
<u>For C</u>:
Since the coefficient of x in the second equation is 1, we will use <u>substitution</u> again.
x+2y=-11
To isolate x, subtract 2y from each side:
x+2y-2y=-11-2y
x=-11-2y
Now substitute this in place of x in the first equation:
-2x-y=-13
-2(-11-2y)-y=-13
Using the distributive property, we have:
-2(-11)-2(-2y)-y=-13
22+4y-y=-13
Combining like terms:
22+3y=-13
Subtract 22 from each side:
22+3y-22=-13-22
3y=-35
Divide both sides by 3:
3y/3 = -35/3
y = -35/3
This is <u>not the y-coordinate</u> of the answer we're looking for, so <u>C is not correct</u>.
<u>For D</u>:
Since the coefficients of x are the same in each equation, we will use <u>elimination</u>. We have 2x in each equation; to eliminate this, we will subtract, since 2x-2x=0:
Divide both sides by -8:
-8y/-8 = -24/-8
y=3
The y-coordinate is correct; next we check the x-coordinate Substitute the value for y into the first equation:
2x-y=7
2x-3=7
Add 3 to each side:
2x-3+3=7+3
2x=10
Divide each side by 2:
2x/2=10/2
x=5
This gives us the x- and y-coordinate we need, so <u>D is the correct answer</u>.
D)
Explanation:
We solve each system to find the correct answer.
<u>For A:</u>
Since we have the coefficients of both variables the same, we will use <u>elimination </u>to solve this.
Since the coefficients of y are -2 and 2, we can add the equations to solve, since -2+2=0 and cancels the y variable:
Next we divide both sides by 6:
6x/6 = 23/6
x = 23/6
This is <u>not the x-coordinate</u> of the answer we are looking for, so <u>A is not correct</u>.
<u>For B</u>:
For this equation, it will be easier to isolate a variable and use <u>substitution</u>, since the coefficient of both x and y in the first equation is 1:
x-y=-2
Add y to both sides:
x-y+y=-2+y
x=-2+y
We now substitute this in place of x in the second equation:
4x-3y=11
4(-2+y)-3y=11
Using the distributive property, we have:
4(-2)+4(y)-3y=11
-8+4y-3y=11
Combining like terms, we have:
-8+y=11
Add 8 to each side:
-8+y+8=11+8
y=19
This is <u>not the y-coordinate</u> of the answer we're looking for, so <u>B is not correct</u>.
<u>For C</u>:
Since the coefficient of x in the second equation is 1, we will use <u>substitution</u> again.
x+2y=-11
To isolate x, subtract 2y from each side:
x+2y-2y=-11-2y
x=-11-2y
Now substitute this in place of x in the first equation:
-2x-y=-13
-2(-11-2y)-y=-13
Using the distributive property, we have:
-2(-11)-2(-2y)-y=-13
22+4y-y=-13
Combining like terms:
22+3y=-13
Subtract 22 from each side:
22+3y-22=-13-22
3y=-35
Divide both sides by 3:
3y/3 = -35/3
y = -35/3
This is <u>not the y-coordinate</u> of the answer we're looking for, so <u>C is not correct</u>.
<u>For D</u>:
Since the coefficients of x are the same in each equation, we will use <u>elimination</u>. We have 2x in each equation; to eliminate this, we will subtract, since 2x-2x=0:
Divide both sides by -8:
-8y/-8 = -24/-8
y=3
The y-coordinate is correct; next we check the x-coordinate Substitute the value for y into the first equation:
2x-y=7
2x-3=7
Add 3 to each side:
2x-3+3=7+3
2x=10
Divide each side by 2:
2x/2=10/2
x=5
This gives us the x- and y-coordinate we need, so <u>D is the correct answer</u>.
Answer:
Step-by-step explanation:
Given
The bag contains 6 orange and 9 lime sweets
For both sweets of the same flavor, Jodi must either choose orange or lime
No. of ways it can be done is
The total no of ways of selecting two sweets out of 15 is
The probability that both sweets are the same flavor