Westonci.ca is the Q&A platform that connects you with experts who provide accurate and detailed answers. Join our platform to connect with experts ready to provide detailed answers to your questions in various areas. Get quick and reliable solutions to your questions from a community of experienced experts on our platform.
Sagot :
To determine the slope and [tex]\( y \)[/tex]-intercept of the linear function passing through the points [tex]\((0, -3)\)[/tex] and [tex]\((6, 15)\)[/tex], we will follow a step-by-step approach.
### Step 1: Determine the slope (m)
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 given by:
[tex]\[ m = \frac{y_2 - y_1}{x_2 - x_1} \][/tex]
Substituting the given points [tex]\((x_1, y_1) = (0, -3)\)[/tex] and [tex]\((x_2, y_2) = (6, 15)\)[/tex] into the formula:
[tex]\[ m = \frac{15 - (-3)}{6 - 0} = \frac{15 + 3}{6} = \frac{18}{6} = 3 \][/tex]
So, the slope [tex]\( m \)[/tex] is 3.
### Step 2: Determine the [tex]\( y \)[/tex]-intercept
The [tex]\( y \)[/tex]-intercept of a linear function is the point where the line crosses the [tex]\( y \)[/tex]-axis. This happens when [tex]\( x = 0 \)[/tex].
From the given points, we already know that one of the points is [tex]\((0, -3)\)[/tex]. This means that the [tex]\( y \)[/tex]-intercept is [tex]\((0, -3)\)[/tex].
### Step 3: Verify the options
Given the slope [tex]\( m = 3 \)[/tex] and the [tex]\( y \)[/tex]-intercept as [tex]\((0, -3)\)[/tex], we can now verify the correct option:
- Option A states the slope is [tex]\(\frac{1}{3}\)[/tex] and the [tex]\( y \)[/tex]-intercept is [tex]\((-3,0)\)[/tex]. This is incorrect.
- Option B states the slope is [tex]\(\frac{1}{3}\)[/tex] and the [tex]\( y \)[/tex]-intercept is [tex]\((0,-3)\)[/tex]. This is incorrect.
- Option C states the slope is 3 and the [tex]\( y \)[/tex]-intercept is [tex]\((0,-3)\)[/tex]. This is correct.
- Option D states the slope is -3 and the [tex]\( y \)[/tex]-intercept is [tex]\((0,-3)\)[/tex]. This is incorrect.
Therefore, the correct answer is:
C. The slope is 3. The [tex]\( y \)[/tex]-intercept is [tex]\((0, -3)\)[/tex].
### Step 1: Determine the slope (m)
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 given by:
[tex]\[ m = \frac{y_2 - y_1}{x_2 - x_1} \][/tex]
Substituting the given points [tex]\((x_1, y_1) = (0, -3)\)[/tex] and [tex]\((x_2, y_2) = (6, 15)\)[/tex] into the formula:
[tex]\[ m = \frac{15 - (-3)}{6 - 0} = \frac{15 + 3}{6} = \frac{18}{6} = 3 \][/tex]
So, the slope [tex]\( m \)[/tex] is 3.
### Step 2: Determine the [tex]\( y \)[/tex]-intercept
The [tex]\( y \)[/tex]-intercept of a linear function is the point where the line crosses the [tex]\( y \)[/tex]-axis. This happens when [tex]\( x = 0 \)[/tex].
From the given points, we already know that one of the points is [tex]\((0, -3)\)[/tex]. This means that the [tex]\( y \)[/tex]-intercept is [tex]\((0, -3)\)[/tex].
### Step 3: Verify the options
Given the slope [tex]\( m = 3 \)[/tex] and the [tex]\( y \)[/tex]-intercept as [tex]\((0, -3)\)[/tex], we can now verify the correct option:
- Option A states the slope is [tex]\(\frac{1}{3}\)[/tex] and the [tex]\( y \)[/tex]-intercept is [tex]\((-3,0)\)[/tex]. This is incorrect.
- Option B states the slope is [tex]\(\frac{1}{3}\)[/tex] and the [tex]\( y \)[/tex]-intercept is [tex]\((0,-3)\)[/tex]. This is incorrect.
- Option C states the slope is 3 and the [tex]\( y \)[/tex]-intercept is [tex]\((0,-3)\)[/tex]. This is correct.
- Option D states the slope is -3 and the [tex]\( y \)[/tex]-intercept is [tex]\((0,-3)\)[/tex]. This is incorrect.
Therefore, the correct answer is:
C. The slope is 3. The [tex]\( y \)[/tex]-intercept is [tex]\((0, -3)\)[/tex].
We hope our answers were helpful. Return anytime for more information and answers to any other questions you may have. Thanks for stopping by. We strive to provide the best answers for all your questions. See you again soon. Keep exploring Westonci.ca for more insightful answers to your questions. We're here to help.
