Systems of Equations from Graphs and Tables Guided Notes

What is the first step in writing a system of equations from a graph?

• Write the equations in slope-intercept form

• Find the point where the lines intersect

• Calculate the slope of each line

• Identify the y-intercept of each line

What does the slope of a line indicate?

• The rate of change between x and y

• The starting point of the line on the graph

• The ending point of the line on the graph

• The total distance the line covers

What role does the y-intercept play in the slope-intercept form of an equation?

• It determines the slope of the line

• It shows the direction of the line

• It represents where the line crosses the y-axis

• It indicates the highest point of the line

How do you convert an equation from slope-intercept form to standard form?

• Divide each term by the y-intercept

• Subtract the x-term from both sides and adjust to make 'a' positive

• Add the slope to both sides of the equation

• Multiply the whole equation by the slope

When converting to standard form, why must 'a' be a positive whole number?

• To simplify the slope calculation

• To make the graph of the line more accurate

• It is a convention for the standard form

• To ensure the equation is easier to solve

What is necessary to write an equation of a line from a table?

• The total number of points in the table

• The x-intercepts of the table

• The maximum and minimum values of the table

• The slope and a point from the table

How do you find the y-intercept in a table?

• By identifying the highest value of y

• By extrapolating the line back to where it crosses the y-axis

• By calculating the slope first

• By finding the point where x is 0

In the context of comparing costs, what does the intersection point of two lines represent?

• The point where one cost becomes greater than the other

• The minimum cost

• The point where both costs are equal

• The maximum cost

What is the slope of a line that represents a constant increase in cost per item?

• The rate of cost increase per item

• The number of items

• The cost of the item

• 0

In a business model comparison, what does the slope represent?

• The cost increase per additional unit

• The profit margin per unit sold

• The initial investment required

• The total revenue generated