Graphing Linear Functions
What is the general shape of a linear function graph? Describe its characteristics and explain how the slope and y-intercept influence the graph's appearance.
straight line
What is the slope of the line y=3/4x+7
3/4
What does the y-intercept represent?
where the line crosses the y-axis
Let f(x)=x; show g(x) for a vertical shift 2 units up.
g(x)=x+2
What is the common difference in the sequence: 10, 15, 20, ...?
5
What is the standard form of a linear equation?
Ax+By=C
How do you find the slope of a line?
change in y over the change in x
What do the letters (m) and (b) represent in the slope-intercept form?
m is the slope; b is the y-intercept
Let f(x)=5x-1; show g(x) for a horizontal shift 4 units to the right. Do not simplify.
What is g(x)=5(x-4)-1.
What is the a1 in the arithmetic sequence: 7, 14, 21, ...?
7
Find the range for the function 9x+3y=12
Domain: -2, -1, 0, 1, 2
10, 7, 4, 1, -2
Given the points (4, 7) and (10, 15), calculate the slope of the line that passes through these points.
4/3
What is the slope-intercept form of a linear equation?
y=mx+b
Let g(x) be a reflection across the y-axis for f(x)=-2x-5; write the equation for g(x).
g(x)=2x-5.
Find the 11th term of the arithmetic sequence: 2, 5, 8, ...
32
Explain how to graph the linear equation y=−3x+2. Include steps for finding the x- and y-intercepts and plotting the line on a graph.
y-intercept is 2, slope is -3/1
What does a slope of 0 indicate about a line?
No matter what value of x you have, you get the same y-value. It does not increase or decrease.
If the slope of a line is -2 and the y-intercept is 5, write the equation of the line in slope-intercept form.
y=-2x+5
Describe the transformations of the function f(x)=(-x)-9
reflected across y-axis, shifted down 9
Write the formula for the nth term of an arithmetic sequence.
an=dn+a1-d or an=a1+(n-1)d
What are the x- and y-intercepts of the linear equation 9x+6y=6
x: (2/3, 0)
y: (0, 1)
Define the concept of slope in your own words. How does the slope affect the steepness and direction of a line? Provide an example with a slope of your choice.
constant change of a linear function, fraction is less steep, m>1, slope is steeper
A line has the equation y−4=2(x+1). Rewrite this equation in slope-intercept form. What are the slope and y-intercept of the line?
y=2x+6
Let f(x)=x; show g(x) for a vertical compression of 1/2 and then h(x) for a horizontal shift 4 units to the left of g(x).
g(x)=1/2x and h(x)=1/2(x+4).
Write an explicit formula for the nth term of the arithmetic sequence that starts with 3 and has a common difference of 4. Then, calculate the 10th term of this sequence.
an=4n-1
39