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## Algebra 1

### 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 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.(18 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.(3 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.(5 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.(12 votes)

- While I understand the idea of economy of space, skipping steps while showing how the problems were worked isn't helpful. It can make the process more confusing.(6 votes)
- what was life like during the blip?(5 votes)
- i am struggling with comparing liner rates even tho i have watch the video a lot of time. do you have any advice that might help me and help me remember?(5 votes)
- I am seven parallel universes ahead of you guys, i am in THE FIRST GRADE.(3 votes)
- The rate equations are a pain(1 vote)
- ti hablo shpaish v obezyana state(1 vote)