IDNLearn.com is designed to help you find the answers you need quickly and easily. Our platform offers detailed and accurate responses from experts, helping you navigate any topic with confidence.
Sagot :
Certainly! Let's write the equation of the line in point-slope form step-by-step.
### Step 1: Understand the Problem
We need to find the equation of a line that falls 7 units for every 11 unit increases in \(x\) and passes through the point (-2, 5).
### Step 2: Determine the Slope
Since the line falls 7 units for every 11 units it increases in \(x\), the rise (\( \Delta y \)) is -7 (because it falls), and the run (\( \Delta x \)) is 11. The slope \(m\) of the line is given by:
[tex]\[ m = \frac{\Delta y}{\Delta x} = \frac{-7}{11} = -0.6363636363636364 \][/tex]
### Step 3: Use the Point-Slope Form
The point-slope form of the equation of a line is:
[tex]\[ y - y_1 = m(x - x_1) \][/tex]
Where \((x_1, y_1)\) is a point on the line and \( m \) is the slope.
Given the point \((-2, 5)\) and the slope \( -0.6363636363636364 \), we can substitute these values into the point-slope form:
[tex]\[ y - 5 = -0.6363636363636364(x - (-2)) \][/tex]
### Step 4: Simplify the Equation
To make the equation clearer:
[tex]\[ y - 5 = -0.6363636363636364(x + 2) \][/tex]
### Summary
So, the equation of the line in point-slope form is:
[tex]\[ y - 5 = -0.6363636363636364(x + 2) \][/tex]
This is the detailed step-by-step solution to writing the equation of the line in point-slope form based on the given conditions.
### Step 1: Understand the Problem
We need to find the equation of a line that falls 7 units for every 11 unit increases in \(x\) and passes through the point (-2, 5).
### Step 2: Determine the Slope
Since the line falls 7 units for every 11 units it increases in \(x\), the rise (\( \Delta y \)) is -7 (because it falls), and the run (\( \Delta x \)) is 11. The slope \(m\) of the line is given by:
[tex]\[ m = \frac{\Delta y}{\Delta x} = \frac{-7}{11} = -0.6363636363636364 \][/tex]
### Step 3: Use the Point-Slope Form
The point-slope form of the equation of a line is:
[tex]\[ y - y_1 = m(x - x_1) \][/tex]
Where \((x_1, y_1)\) is a point on the line and \( m \) is the slope.
Given the point \((-2, 5)\) and the slope \( -0.6363636363636364 \), we can substitute these values into the point-slope form:
[tex]\[ y - 5 = -0.6363636363636364(x - (-2)) \][/tex]
### Step 4: Simplify the Equation
To make the equation clearer:
[tex]\[ y - 5 = -0.6363636363636364(x + 2) \][/tex]
### Summary
So, the equation of the line in point-slope form is:
[tex]\[ y - 5 = -0.6363636363636364(x + 2) \][/tex]
This is the detailed step-by-step solution to writing the equation of the line in point-slope form based on the given conditions.
Your engagement is important to us. Keep sharing your knowledge and experiences. Let's create a learning environment that is both enjoyable and beneficial. IDNLearn.com has the solutions to your questions. Thanks for stopping by, and come back for more insightful information.