Looking for reliable answers? Westonci.ca is the ultimate Q&A platform where experts share their knowledge on various topics. Join our platform to connect with experts ready to provide accurate answers to your questions in various fields. Explore comprehensive solutions to your questions from knowledgeable professionals across various fields on our platform.
Sagot :
To determine the type of slope for the line that passes through each pair of given points, we can follow a step-by-step process. Recall that the slope of a line between two points [tex]\((x_1, y_1)\)[/tex] and [tex]\((x_2, y_2)\)[/tex] is given by:
[tex]\[ \text{slope} = \frac{y_2 - y_1}{x_2 - x_1} \][/tex]
Let's analyze each pair of points:
1. Points [tex]\((-7, 8)\)[/tex] and [tex]\((-7, 0)\)[/tex]
- Here, [tex]\(x_1 = x_2 = -7\)[/tex]. When the x-coordinates are the same, the line is vertical.
- The slope of a vertical line is undefined.
- Therefore, the slope is undefined.
2. Points [tex]\((3, 5)\)[/tex] and [tex]\((-1, 2)\)[/tex]
- Calculate the slope: [tex]\(\frac{2 - 5}{-1 - 3} = \frac{-3}{-4} = \frac{3}{4}\)[/tex].
- Because the result is positive, the slope is positive.
- Therefore, the slope is positive.
3. Points [tex]\((6, -3)\)[/tex] and [tex]\((-4, -3)\)[/tex]
- Here, [tex]\(y_1 = y_2 = -3\)[/tex]. When the y-coordinates are the same, the line is horizontal.
- The slope of a horizontal line is zero.
- Therefore, the slope is zero.
4. Points [tex]\((2, 4)\)[/tex] and [tex]\((5, 1)\)[/tex]
- Calculate the slope: [tex]\(\frac{1 - 4}{5 - 2} = \frac{-3}{3} = -1\)[/tex].
- Because the result is negative, the slope is negative.
- Therefore, the slope is negative.
To summarize:
- The slope for the line through points [tex]\((-7, 8)\)[/tex] and [tex]\((-7, 0)\)[/tex] is undefined.
- The slope for the line through points [tex]\((3, 5)\)[/tex] and [tex]\((-1, 2)\)[/tex] is positive.
- The slope for the line through points [tex]\((6, -3)\)[/tex] and [tex]\((-4, -3)\)[/tex] is zero.
- The slope for the line through points [tex]\((2, 4)\)[/tex] and [tex]\((5, 1)\)[/tex] is negative.
[tex]\[ \text{slope} = \frac{y_2 - y_1}{x_2 - x_1} \][/tex]
Let's analyze each pair of points:
1. Points [tex]\((-7, 8)\)[/tex] and [tex]\((-7, 0)\)[/tex]
- Here, [tex]\(x_1 = x_2 = -7\)[/tex]. When the x-coordinates are the same, the line is vertical.
- The slope of a vertical line is undefined.
- Therefore, the slope is undefined.
2. Points [tex]\((3, 5)\)[/tex] and [tex]\((-1, 2)\)[/tex]
- Calculate the slope: [tex]\(\frac{2 - 5}{-1 - 3} = \frac{-3}{-4} = \frac{3}{4}\)[/tex].
- Because the result is positive, the slope is positive.
- Therefore, the slope is positive.
3. Points [tex]\((6, -3)\)[/tex] and [tex]\((-4, -3)\)[/tex]
- Here, [tex]\(y_1 = y_2 = -3\)[/tex]. When the y-coordinates are the same, the line is horizontal.
- The slope of a horizontal line is zero.
- Therefore, the slope is zero.
4. Points [tex]\((2, 4)\)[/tex] and [tex]\((5, 1)\)[/tex]
- Calculate the slope: [tex]\(\frac{1 - 4}{5 - 2} = \frac{-3}{3} = -1\)[/tex].
- Because the result is negative, the slope is negative.
- Therefore, the slope is negative.
To summarize:
- The slope for the line through points [tex]\((-7, 8)\)[/tex] and [tex]\((-7, 0)\)[/tex] is undefined.
- The slope for the line through points [tex]\((3, 5)\)[/tex] and [tex]\((-1, 2)\)[/tex] is positive.
- The slope for the line through points [tex]\((6, -3)\)[/tex] and [tex]\((-4, -3)\)[/tex] is zero.
- The slope for the line through points [tex]\((2, 4)\)[/tex] and [tex]\((5, 1)\)[/tex] is negative.
We appreciate your time. Please revisit us for more reliable answers to any questions you may have. We hope our answers were useful. Return anytime for more information and answers to any other questions you have. Westonci.ca is committed to providing accurate answers. Come back soon for more trustworthy information.
