Unitary Method
The word “unitary” comes from the word “unit”, which means a single and complete entity. In this method, we find the value of a unit product from the given number of products, and then we solve for the other number of products.
Speed, Time, and Distance
Imagine you and 3 of your friends are planning to go to the playground at 6 in the evening. Your house is one mile away from the playground and one of your friends named Jim must start at 5 pm to reach the playground by walk. The other two friends are 3 miles away.
Profit and Loss
The amount earned or lost on the sale of one or more items is referred to as the profit or loss on that item.
Units and Measurements
Measurements and comparisons are the foundation of science and engineering. We, therefore, need rules that tell us how things are measured and compared. For these measurements and comparisons, we perform certain experiments, and we will need the experiments to set up the devices.
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### Algebra Exercise: Writing the Equation in Slope-Intercept Form
**Problem 3.7.47:**
**Task:**
Write the equation in slope-intercept form.
Given equation:
\[ 4x + 3y = 18 \]
\[ y = \_\]
(Use integers or fractions for any numbers in the equation.)
**Instructions:**
Enter your answer in the answer box and then click "Check Answer."
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**Explanation of Slope-Intercept Form:**
The slope-intercept form of a linear equation is given by:
\[ y = mx + b \]
where:
- \( m \) represents the slope of the line.
- \( b \) represents the y-intercept (the point where the line crosses the y-axis).
To convert the given equation into slope-intercept form, follow these steps:
1. Isolate \( y \) on one side of the equation.
2. Simplify the equation to get it into the form \( y = mx + b \).
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**Note:**
There are no graphs or diagrams associated with this problem.
**Solution Steps:**
1. Start with the given equation:
\[ 4x + 3y = 18 \]
2. Subtract \( 4x \) from both sides to isolate the term containing \( y \):
\[ 3y = -4x + 18 \]
3. Divide every term by 3 to solve for \( y \):
\[ y = -\frac{4}{3}x + 6 \]
So, the equation in slope-intercept form is:
\[ y = -\frac{4}{3}x + 6 \]
Enter this equation into the answer box and click "Check Answer" to verify your solution.
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**References:**
This problem is adapted from a standard algebra exercise on converting equations to slope-intercept form.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fd6344eb2-25f9-4734-a70a-fbc48b5f93b4%2F4c7b3e74-b441-47f6-8707-3272d4c88a1f%2Famardbd_processed.jpeg&w=3840&q=75)
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