GRAPHS
What is the slope of the line represented by the equation y=2x+3y=2x+3?
2
What is the first term in the table values for the linear function y=4x+2y=4x+2 when x=1x=1?
6
What does the term "slope" represent in a linear function?
The steepness of the line, indicating how much y changes for a unit change in x.
What is a real-world example of a situation that can be modeled with a linear function?
The relationship between distance and time when traveling at a constant speed.
Identify the y-intercept of the graph of the equation y=−x+5y=−x+5.
5
Fill in the table for the function y=−2x+6y=−2x+6 for x=0,1,2,3?
The table values are 6, 4, 2, 0.
Write the equation of a line in slope-intercept form with a slope of 2 and a y-intercept of -4.
y=2x−4
How can a linear function be represented in a verbal description? Give an example.
"For every hour worked, I earn $15."
Sketch the graph of the equation y=12x−1y=21x−1. What are the coordinates of the x-intercept?
The x-intercept is (2, 0)
How can you determine the slope from a table of values for a linear function?
Subtract the y-values and divide by the difference in x-values between two points.
If f(x)=3x+1, what is f(2)?
7
Describe how you would interpret the slope in a graph representing distance over time.
The slope represents the speed or rate of travel.
Determine the equation of the line that passes through the points (2, 3) and (4, 7).
y=2x−1
Given the table below, write the equation of the line.
y=2x+1
How do you convert the equation 2y−4x=8 into slope-intercept form?
y=2x+4
What is the difference between a linear function and a nonlinear function in terms of their graphs?
Linear functions produce straight lines, while nonlinear functions create curves.
Describe how the graph of y=3x−1y=3x−1 changes when compared to the graph of y=3xy=3x.
The graph shifts down by 1 unit.
Explain how to identify whether a table of values represents a linear function.
If the differences between consecutive y-values divided by the differences between consecutive x-values are constant, it represents a linear function.
Explain the significance of the y-intercept in a real-world scenario involving linear functions.
It represents the initial value or starting point of the relationship when x is zero.
Explain how to use a linear equation to predict future values in a data set.
By inputting future x-values into the equation, you can calculate corresponding y-values to make predictions.