Question
choose the equation that has a slope of -1 and a y intercept of 5.
a.) y=5x-1
b.) y=-x+5
c.) y=x-5
d.) x=x-5
a.) y=5x-1
b.) y=-x+5
c.) y=x-5
d.) x=x-5
Answers
Answer
choose all the equations that are written in slope intercept form. choose 2 options.
A.) y+3x
b.) -5y=2x+12
c.) 5x+4y=20
d.) x=8y-9
e.) y=-x+1
A.) y+3x
b.) -5y=2x+12
c.) 5x+4y=20
d.) x=8y-9
e.) y=-x+1
Answer
what are the two answers???
Answer
what is the distance from (5, 5) to (8, 9). round to the nearest 10th
Answer
find the distance between point m(-2, 9) and n(8, 12). round to your answer to the 10th
Answer
what is the distance from (5, 3) to (15, 10). round your answer to the nearest 10th
Answered by
GPT-4 Turbo
The slope-intercept form of a linear equation is y = mx + b, where m is the slope and b is the y-intercept.
Given a slope of -1 and a y-intercept of 5, the equation will be:
y = -1x + 5, which simplifies to:
y = -x + 5
So the correct choice is:
b.) y = -x + 5
Given a slope of -1 and a y-intercept of 5, the equation will be:
y = -1x + 5, which simplifies to:
y = -x + 5
So the correct choice is:
b.) y = -x + 5
Answered by
GPT-4 Turbo
The slope-intercept form of a linear equation is written as y = mx + b, where m is the slope and b is the y-intercept.
Looking at the given options:
A.) y + 3x is incomplete and does not represent an equation in slope-intercept form.
B.) -5y = 2x + 12 can be converted to slope-intercept form by dividing all terms by -5 to isolate y; hence, not initially in slope-intercept form.
C.) 5x + 4y = 20 can be converted to slope-intercept form by isolating y; thus not in slope-intercept form.
D.) x = 8y - 9 represents a linear equation, but is not in slope-intercept form as it is solved for x rather than y.
E.) y = -x + 1 is already in the slope-intercept form.
Therefore the options that are already in slope-intercept form are:
E.) y = -x + 1
To complete this, we need to convert the options B.) and C.) to slope-intercept form to determine if any of them can also be valid.
Starting with B.):
-5y = 2x + 12
Divide all terms by -5:
y = (-2/5)x - 12/5
After this transformation, it is now in slope-intercept form.
C.) does not need to be considered further as we've already found two options in slope-intercept form.
Thus, the two options that are (or can be easily converted to) slope-intercept form are:
B.) -5y = 2x + 12 (after converting)
E.) y = -x + 1
If the specific requirement is the equations that are already written in slope-intercept form without needing conversion, then the correct option is only:
E.) y = -x + 1
Looking at the given options:
A.) y + 3x is incomplete and does not represent an equation in slope-intercept form.
B.) -5y = 2x + 12 can be converted to slope-intercept form by dividing all terms by -5 to isolate y; hence, not initially in slope-intercept form.
C.) 5x + 4y = 20 can be converted to slope-intercept form by isolating y; thus not in slope-intercept form.
D.) x = 8y - 9 represents a linear equation, but is not in slope-intercept form as it is solved for x rather than y.
E.) y = -x + 1 is already in the slope-intercept form.
Therefore the options that are already in slope-intercept form are:
E.) y = -x + 1
To complete this, we need to convert the options B.) and C.) to slope-intercept form to determine if any of them can also be valid.
Starting with B.):
-5y = 2x + 12
Divide all terms by -5:
y = (-2/5)x - 12/5
After this transformation, it is now in slope-intercept form.
C.) does not need to be considered further as we've already found two options in slope-intercept form.
Thus, the two options that are (or can be easily converted to) slope-intercept form are:
B.) -5y = 2x + 12 (after converting)
E.) y = -x + 1
If the specific requirement is the equations that are already written in slope-intercept form without needing conversion, then the correct option is only:
E.) y = -x + 1
Answered by
GPT-4 Turbo
I apologize for the misstep in my last response. The question indeed asks for the equations that are already written in slope-intercept form.
The slope-intercept form of a linear equation is y = mx + b.
Given this, the two options that are in slope-intercept form are:
B.) -5y = 2x + 12 (can be converted, but initially not in slope-intercept form)
and
E.) y = -x + 1 (already in slope-intercept form)
Upon re-evaluation, it appears that while option B can be in slope-intercept form after converting, it is not currently written in that form. Only option E is written in the correct form as it stands.
Therefore, the correct answer should be:
E.) y = -x + 1
Given that we must choose two options that are written in slope-intercept form and there appears to be only one (E) in the list provided, it's possible there's an oversight in the given choices, or there's an error in one of the options. For instance, option A could be a typo, and if it's supposed to be y = -3x, then it would be in slope-intercept form. However, with the provided options, only E is definitely in slope-intercept form, as it is presented.
The slope-intercept form of a linear equation is y = mx + b.
Given this, the two options that are in slope-intercept form are:
B.) -5y = 2x + 12 (can be converted, but initially not in slope-intercept form)
and
E.) y = -x + 1 (already in slope-intercept form)
Upon re-evaluation, it appears that while option B can be in slope-intercept form after converting, it is not currently written in that form. Only option E is written in the correct form as it stands.
Therefore, the correct answer should be:
E.) y = -x + 1
Given that we must choose two options that are written in slope-intercept form and there appears to be only one (E) in the list provided, it's possible there's an oversight in the given choices, or there's an error in one of the options. For instance, option A could be a typo, and if it's supposed to be y = -3x, then it would be in slope-intercept form. However, with the provided options, only E is definitely in slope-intercept form, as it is presented.
Answered by
GPT-4 Turbo
To calculate the distance between two points in a Cartesian coordinate system, you can use the distance formula, which is derived from the Pythagorean theorem. The distance between two points (x1, y1) and (x2, y2) is given by:
d = √[(x2 - x1)² + (y2 - y1)²]
For the points (5, 5) and (8, 9):
d = √[(8 - 5)² + (9 - 5)²]
= √[(3)² + (4)²]
= √[9 + 16]
= √[25]
= 5
So the distance between the points (5, 5) and (8, 9) is exactly 5 units, meaning there is no need to round to the nearest 10th.
d = √[(x2 - x1)² + (y2 - y1)²]
For the points (5, 5) and (8, 9):
d = √[(8 - 5)² + (9 - 5)²]
= √[(3)² + (4)²]
= √[9 + 16]
= √[25]
= 5
So the distance between the points (5, 5) and (8, 9) is exactly 5 units, meaning there is no need to round to the nearest 10th.
Answered by
GPT-4 Turbo
To find the distance between two points, M(-2, 9) and N(8, 12), we use the distance formula:
\[ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \]
Where (x1, y1) are the coordinates of the first point and (x2, y2) are the coordinates of the second point.
For points M(-2, 9) and N(8, 12):
\[ d = \sqrt{(8 - (-2))^2 + (12 - 9)^2} \]
\[ d = \sqrt{(8 + 2)^2 + (12 - 9)^2} \]
\[ d = \sqrt{10^2 + 3^2} \]
\[ d = \sqrt{100 + 9} \]
\[ d = \sqrt{109} \]
Now calculate the square root of 109 and round to the nearest tenth:
\[ d ≈ \sqrt{109} ≈ 10.4 \] (rounded to the nearest tenth)
Thus, the distance between points M and N, rounded to the nearest tenth, is approximately 10.4 units.
\[ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \]
Where (x1, y1) are the coordinates of the first point and (x2, y2) are the coordinates of the second point.
For points M(-2, 9) and N(8, 12):
\[ d = \sqrt{(8 - (-2))^2 + (12 - 9)^2} \]
\[ d = \sqrt{(8 + 2)^2 + (12 - 9)^2} \]
\[ d = \sqrt{10^2 + 3^2} \]
\[ d = \sqrt{100 + 9} \]
\[ d = \sqrt{109} \]
Now calculate the square root of 109 and round to the nearest tenth:
\[ d ≈ \sqrt{109} ≈ 10.4 \] (rounded to the nearest tenth)
Thus, the distance between points M and N, rounded to the nearest tenth, is approximately 10.4 units.
Answered by
GPT-4 Turbo
To calculate the distance between two points (x1, y1) and (x2, y2), use the distance formula, which is:
\[ d = \sqrt{ (x2 - x1)^2 + (y2 - y1)^2 } \]
For the points (5, 3) and (15, 10):
\[ d = \sqrt{ (15 - 5)^2 + (10 - 3)^2 } \]
\[ d = \sqrt{ (10)^2 + (7)^2 } \]
\[ d = \sqrt{ 100 + 49 } \]
\[ d = \sqrt{ 149 } \]
The exact square root of 149 is a non-terminating decimal, so we round it to the nearest tenth:
\[ d ≈ \sqrt{149} ≈ 12.2 \] (rounded to the nearest tenth)
Therefore, the distance between the points (5, 3) and (15, 10), rounded to the nearest tenth, is approximately 12.2 units.
\[ d = \sqrt{ (x2 - x1)^2 + (y2 - y1)^2 } \]
For the points (5, 3) and (15, 10):
\[ d = \sqrt{ (15 - 5)^2 + (10 - 3)^2 } \]
\[ d = \sqrt{ (10)^2 + (7)^2 } \]
\[ d = \sqrt{ 100 + 49 } \]
\[ d = \sqrt{ 149 } \]
The exact square root of 149 is a non-terminating decimal, so we round it to the nearest tenth:
\[ d ≈ \sqrt{149} ≈ 12.2 \] (rounded to the nearest tenth)
Therefore, the distance between the points (5, 3) and (15, 10), rounded to the nearest tenth, is approximately 12.2 units.
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