Question

study guide algebra 1 unit 3: linear equations
study all of the following concepts for the test.
key topics to study
● creating equations
○ how to put equations in words first
○ how to define variables
○ creating the final equation with variables and numbers
● standard form
○ ax + by = c where a, b, and c are all integers
○ how to convert between standard form, point - slope form, and slope intercept form using algebra
○ how to find the x and y axis
○ graphing real world situations in standard form
● domain and range of functions
○ domain--all possible x values
○ range--all possible y values
○ continuous--the domain includes all real numbers in an interval
○ discrete--only select numbers are included in the domain
○ one - to - one = each element of the domain (x) has exactly one output (y)
○ function--a relationship where each input (x) has exactly one output (y).
■ note--the opposite does not have to be true.
● linear functions
○ replace y with f(x) meaning \a function of x\
■ they have identical values and graphs
○ ex. y = 2x is the same as f(x) = 2x
overview of key concepts
how to create an equations from words examples
find out how far jack went if he drives 70 miles per hour for 3 hours.

x = miles traveled
70 = x/3
x = 70(3) = 210

Explanation:

Step1: Identify the formula

The formula for average speed is \( \text{Average Speed}=\frac{\text{Total miles}}{\text{Total time}} \).

Step2: Substitute the values

Given average speed \( = 70\) miles per hour and total time \(=3\) hours. Let \(x\) be the total miles. So, \(70=\frac{x}{3}\).

Step3: Solve for \(x\)

Multiply both sides of the equation \(70=\frac{x}{3}\) by \(3\). We get \(x = 70\times3\).

Answer:

\(x = 210\) miles.