Westonci.ca is the premier destination for reliable answers to your questions, brought to you by a community of experts. Connect with a community of professionals ready to provide precise solutions to your questions quickly and accurately. Discover detailed answers to your questions from a wide network of experts on our comprehensive Q&A platform.
Sagot :
Let's solve this step by step.
1. Calculate the slope of the line passing through (66,33) and (99,51)
The formula for the slope [tex]\(m\)[/tex] between two points [tex]\((x_1, y_1)\)[/tex] and [tex]\((x_2, y_2)\)[/tex] is:
[tex]\[ m = \frac{y_2 - y_1}{x_2 - x_1} \][/tex]
Substituting the given points [tex]\((66, 33)\)[/tex] and [tex]\((99, 51)\)[/tex]:
[tex]\[ m = \frac{51 - 33}{99 - 66} = \frac{18}{33} = \frac{6}{11} \][/tex]
So, the slope [tex]\(m\)[/tex] is [tex]\( \boxed{\frac{6}{11}} \)[/tex].
2. Write the equation of this line in point-slope form
The point-slope form of the equation of a line is given by:
[tex]\[ y - y_1 = m(x - x_1) \][/tex]
Using one of the given points [tex]\((66, 33)\)[/tex] and the slope [tex]\(\frac{6}{11}\)[/tex]:
[tex]\[ y - 33 = \frac{6}{11}(x - 66) \][/tex]
Thus, the point-slope form is [tex]\( \boxed{y - 33 = \frac{6}{11}(x - 66)} \)[/tex].
3. Write the equation of this line in slope-intercept form
The slope-intercept form of a line is:
[tex]\[ y = mx + b \][/tex]
To find [tex]\(b\)[/tex], we use one of the given points and the slope. Again using the point [tex]\((66, 33)\)[/tex] and the slope [tex]\(\frac{6}{11}\)[/tex]:
Substitute [tex]\(x = 66\)[/tex], [tex]\(y = 33\)[/tex], and [tex]\(m = \frac{6}{11}\)[/tex] into the slope-intercept form:
[tex]\[ 33 = \frac{6}{11}(66) + b \][/tex]
[tex]\[ 33 = 6 \times 6 + b \][/tex]
[tex]\[ 33 = 36 + b \][/tex]
Solving for [tex]\(b\)[/tex], we get:
[tex]\[ b = 33 - 36 = -3 \][/tex]
Thus, the slope-intercept form is [tex]\( \boxed{y = \frac{6}{11}x - 3} \)[/tex].
4. Determine if the line passes through the point [tex]\((-11, -8)\)[/tex]
We need to check if the point [tex]\((-11, -8)\)[/tex] satisfies the equation of the line:
Using the slope-intercept form [tex]\(y = \frac{6}{11}x - 3\)[/tex], substitute [tex]\(x = -11\)[/tex] and see if [tex]\(y\)[/tex] equals [tex]\(-8\)[/tex]:
[tex]\[ y = \frac{6}{11}(-11) - 3 = -6 - 3 = -9 \][/tex]
Since [tex]\(-9 \neq -8\)[/tex], the point [tex]\((-11, -8)\)[/tex] does not lie on the line.
Therefore, the answer is [tex]\( \boxed{\text{A. No}} \)[/tex].
1. Calculate the slope of the line passing through (66,33) and (99,51)
The formula for the slope [tex]\(m\)[/tex] between two points [tex]\((x_1, y_1)\)[/tex] and [tex]\((x_2, y_2)\)[/tex] is:
[tex]\[ m = \frac{y_2 - y_1}{x_2 - x_1} \][/tex]
Substituting the given points [tex]\((66, 33)\)[/tex] and [tex]\((99, 51)\)[/tex]:
[tex]\[ m = \frac{51 - 33}{99 - 66} = \frac{18}{33} = \frac{6}{11} \][/tex]
So, the slope [tex]\(m\)[/tex] is [tex]\( \boxed{\frac{6}{11}} \)[/tex].
2. Write the equation of this line in point-slope form
The point-slope form of the equation of a line is given by:
[tex]\[ y - y_1 = m(x - x_1) \][/tex]
Using one of the given points [tex]\((66, 33)\)[/tex] and the slope [tex]\(\frac{6}{11}\)[/tex]:
[tex]\[ y - 33 = \frac{6}{11}(x - 66) \][/tex]
Thus, the point-slope form is [tex]\( \boxed{y - 33 = \frac{6}{11}(x - 66)} \)[/tex].
3. Write the equation of this line in slope-intercept form
The slope-intercept form of a line is:
[tex]\[ y = mx + b \][/tex]
To find [tex]\(b\)[/tex], we use one of the given points and the slope. Again using the point [tex]\((66, 33)\)[/tex] and the slope [tex]\(\frac{6}{11}\)[/tex]:
Substitute [tex]\(x = 66\)[/tex], [tex]\(y = 33\)[/tex], and [tex]\(m = \frac{6}{11}\)[/tex] into the slope-intercept form:
[tex]\[ 33 = \frac{6}{11}(66) + b \][/tex]
[tex]\[ 33 = 6 \times 6 + b \][/tex]
[tex]\[ 33 = 36 + b \][/tex]
Solving for [tex]\(b\)[/tex], we get:
[tex]\[ b = 33 - 36 = -3 \][/tex]
Thus, the slope-intercept form is [tex]\( \boxed{y = \frac{6}{11}x - 3} \)[/tex].
4. Determine if the line passes through the point [tex]\((-11, -8)\)[/tex]
We need to check if the point [tex]\((-11, -8)\)[/tex] satisfies the equation of the line:
Using the slope-intercept form [tex]\(y = \frac{6}{11}x - 3\)[/tex], substitute [tex]\(x = -11\)[/tex] and see if [tex]\(y\)[/tex] equals [tex]\(-8\)[/tex]:
[tex]\[ y = \frac{6}{11}(-11) - 3 = -6 - 3 = -9 \][/tex]
Since [tex]\(-9 \neq -8\)[/tex], the point [tex]\((-11, -8)\)[/tex] does not lie on the line.
Therefore, the answer is [tex]\( \boxed{\text{A. No}} \)[/tex].
Thank you for trusting us with your questions. We're here to help you find accurate answers quickly and efficiently. Your visit means a lot to us. Don't hesitate to return for more reliable answers to any questions you may have. Westonci.ca is here to provide the answers you seek. Return often for more expert solutions.