Interpret The Slope And Y-Intercept Of A Linear Function Word Problems Worksheet

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To interpret the slope and y-intercept of a linear function in word problems, understand that the slope represents the rate of change, showing how much $$y$$ increases or decreases as $$x$$ changes. The y-intercept is the starting value of $$y$$ when $$x$$ is zero. These elements help explain real-world relationships, like growth rates or initial amounts, as demonstrated in write a linear function word problems with solutions.

Algebra 1
Linear Relationship

How Will This Worksheet on "Interpret the Slope and y-Intercept of a Linear Function Word Problems" Benefit Your Student's Learning?

• Helps students apply math to everyday situations, like calculating costs or tracking changes over time.
• Breaks down problems into simple parts using slope and y-intercept, improving problem-solving skills.
• Teaches students to read and understand graphs, useful in various subjects and daily life.
• Develops critical thinking skills by analyzing data, making predictions, and understanding connections.
• Makes math relatable, useful, and enjoyable by connecting concepts to real-life scenarios.

How to Interpret the Slope and y-Intercept of a Linear Function Word Problems?

• First, find the slope (often represented by m) in the equation y=mx+b. The slope shows how much y changes for each increase of 1 in x. It represents the rate of change.
• Then, find the y-intercept (represented by b) in the equation y=mx+b. The y-intercept is the value of y when x is zero. It represents the starting point or initial value.
• After that, determine what the slope and y-intercept mean in the context of the word problem. For example, the slope could represent the cost per item, and the y-intercept could be the initial fee.
• At the end, use the slope and y-intercept to answer questions in the word problem, such as calculating future values or understanding trends.

Solved Example

Q. Alice is a repair technician for a phone company. Each week, she receives a batch of phones that need repairs. The number of phones that she has left to fix at the end of each day can be estimated with the equation $P = 108 - 23d$, where $P$ is the number of phones left and $d$ is the number of days she has worked that week. What is the meaning of the value $108$ in this equation?$\newline$A) Alice will complete the repairs within $108$ days.$\newline$B) Alice starts each week with $108$ phones to fix.$\newline$C) Alice repairs phones at a rate of $108$ per hour.$\newline$D) Alice repairs phones at a rate of $108$ per day.
Solution:
1. Identify Variables and Equation: Identify given variables and equation.$\newline$ Given: $P$ $=$ number of phones left$\newline$ $d$ $=$ number of days worked$\newline$ Equation: $P = 108 - 23d$
2. Understand Equation Structure: Understand the equation structure.$\newline$ $P = 108 - 23d$$\newline$ Number of phones left = Initial number of phones - Number of phones repaired
3. Determine Meaning of $108$: Determine the meaning of $108$. $108$ represents the initial number of phones Alice starts with each week.
4. Match Meaning with Options: Match the meaning with the given options. B) Alice starts each week with $108$ phones to fix.

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