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### Course: Algebra 1>Unit 4

Lesson 6: Modeling with linear equations and inequalities

# Linear equations & graphs: FAQ

## What is a two-variable linear equation?

A two-variable linear equation is an equation with two unknowns (usually represented by $x$ and $y$) that can be graphed as a straight line on a coordinate plane.

## What is slope?

Slope is a measure of the steepness of a line. We calculate it by dividing the change in $y$-values by the change in $x$-values between two points on a line.
Practice with our Slope from graph exercise.
Practice with our Slope in a table exercise.

## What are horizontal and vertical lines?

Horizontal lines are lines that have a slope of $0$, meaning they don't go up or down, while vertical lines have an undefined slope, meaning they don't go left or right.

## What are $x$‍ -intercepts and $y$‍ -intercepts?

The $x$-intercept is the point where a graph crosses the $x$-axis, while the $y$-intercept is the point where a graph crosses the $y$-axis.

## What do we mean by modeling with linear equations and inequalities?

Modeling with linear equations and inequalities means using those mathematical concepts to represent or explain real-world situations.

## Why do we need to learn about linear equations and graphs?

Linear equations and graphs come up all the time in mathematics, science, engineering, and business. They're one of the foundational skills for understanding algebra and more advanced math courses. Plus, they can be really useful for modeling real-world situations and solving problems.

## Want to join the conversation?

• Please further explain the topic of comparing linear rates.
• the way I did it was just to manually compute the numbers without the equation. I put the two rates into a graph with a bar for each rate, a bar for elapsed time or distance, and a bar for how much time or distance I add. I then keep adding distance or time until I find the correct amount.
• I am having a hard time solving "Comparing linear rates word problems" even though I have mastered the previous Units and Lessons. Any suggestions?
Thank you.
• Try to make a table. That's my biggest advice.

Example of a question: So, let's say Company ABC makes 1 million dollars per year. Every year, it increases by 1 million. And let's also say company XYZ makes 5 million but increases by 50% yearly. What is the first year in which company XYZ makes more money?

Solution:
Create a table for both equations. This makes it much easier to look at.

Company ABC:
Year 1: 10 million
Year 2: 11 million
Year 3: 12 million
Year 4: 13 million

Company XYZ:
Year 1: 5 million
Year 2: 7.5 million
Year 3: 11.25 million
Year 4: 16.875 million

As you can see year 4 would be the first year company XYZ makes more money.

Let me know if you need more help.
• what was life like during the blip?
• Hard
• Same for me. I have had great success with Khan Academy but I am hitting a roadblock with rate and linear comparions even tough I passed all related sections to rates and ratios. I am not sure if there is something related to time, distance and time I am missing but i have looking in other place to piece together this concept and am wondering there are any videos I may have missed. Because I usually dont have any issues following along. Even if something is hard or new and takes time it makes sense but this one I a bit lost as to how to set up these equations to to know instinctively what I need to do or how use the information given to set up the equation to solve these types of problems. Its easier when its rate, time and distance but when its bananan's beads and jewerly the chart for rate distance and time I become confused on how to apply it to non traditional word problems.
• This unit was not very hard to learn and understand, but I needed a clearer understanding of Comparing Linear Rates. Please explain this topic in more detail, as I have been having difficulty grasping it for a while. Thank you.
• When dealing with rates why do we sometimes write it as a whole number next to a fraction like 90 km/h and then in other equations we write it as one big fraction like 90 km / 1 hr? Is there a rule to help identify when a particular notation is required?