Understanding Equations from Graphs

This video tutorial teaches how to write equations from graphs by identifying patterns in data. It covers both additive and multiplicative relationships, using examples to illustrate how to derive equations from ordered pairs. The lesson also explains the use of coordinate planes and quadrants, and concludes with a final example to reinforce the concepts.

What is the first step in writing an equation from a graph?

• Calculate the y-intercept

• Draw a line through the points

• Make a table of values from ordered pairs

• Identify the slope of the graph

How can you remember the order of quadrants in a coordinate plane?

• By the color of the quadrants

• By the direction of the letter 'C'

• By the size of the quadrants

• By the number of points in each quadrant

In the county fair example, what does the variable 'r' represent?

• Total money spent

• Number of rides

• Entrance fee

• Money spent on rides

What type of relationship is shown when the total is always ten dollars more than the rides?

• Exponential

• Additive

• Multiplicative

• Logarithmic

What is the equation derived from the county fair example?

• t = r - 10

• t = r + 10

• t = 10r

• t = r / 10

How do you determine if a pattern is multiplicative?

• By subtracting a constant from each value

• By dividing the dependent value by the independent value

• By multiplying each value by a constant

• By adding a constant to each value

What is the equation for the relationship where y is always 2.5 times x?

• y = 2.5 + x

• y = 2.5x

• y = x / 2.5

• y = x - 2.5

In the final example, what is the pattern observed between x and y?

• y is always x minus 2

• y is always x plus 3

• y is always 2 times x

• y is always 3 times x

What is the equation for the final example where y is twice the value of x?

• y = x - 2

• y = x / 2

• y = 2x

• y = 2 + x

How can you verify if your equation is correct?

• By comparing it to another equation

• By drawing a new graph

• By substituting values of x and y into the equation

• By checking if the graph is a straight line