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### Course: Algebra 1 > Unit 4

Lesson 6: Modeling with linear equations and inequalities# Linear equations & graphs: FAQ

Frequently asked questions about linear equations & graphs

## 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.

Practice with our Solutions to 2-variable equations
exercise.

## 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.

Practice with our Slope from two points
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.

Practice with our Horizontal & vertical lines
exercise.

## 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.

Practice with our Intercepts from a graph
exercise.

Practice with our Intercepts from an equation
exercise.

## 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.

Practice with our Comparing linear rates word problems
exercise.

## 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.

Practice with our Relating linear contexts to graph features
exercise.

Practice with our Graphing linear relationships word problems
exercise.

## Want to join the conversation?

- Please further explain the topic of comparing linear rates.(41 votes)
- 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.(11 votes)

- 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.(18 votes)- 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.(32 votes)

- what was life like during the blip?(11 votes)
- 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.(12 votes)
- 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.(12 votes)
- 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?(6 votes)
- Personally, I just use it because it helps with cancelling out the symbol or making sure I don't cancel the wrong thing as far as rules are concerned I don't think there are any rules for that except for the final answer where you have to mention the metric (km, hour, min, km/h, etc).(3 votes)

- Was it just me or was comparing linear rates the hardest part of this whole unit? I need more explaining than one video please. Have a good day! :3(5 votes)
- I don't get it. A triangle with angle x degrees and its opposite side has a length of five, an angle of eighty-eight degrees and its opposite side has a length of six point nine, and its third side has a length of five. What is the X?(3 votes)
- They may want you to consider that a triangle with 2 sides of equal length has equal base angles. So, in your example X + the other base angle + 88° = 180°. The base angles are the same so, 2x° + 88° = 180°. Solve for x. [ X = 46°](2 votes)

- Im fine with getting attempted on this lesson, by observation of the comments it is clear this is out of my skill level.(3 votes)
- I'm having a hard time with comparing linear rates word problems. My math is always incorrect, can someone please explain it to me more??(2 votes)