The equation of a line & Inequalities
X and Y Intercepts
Definitions
Equations of Line +Point of intersection
Transformations of a line
100
For the following line, state the y-intercept in coordinate form? y=2x-5
(0,-5)
100
Find the x-intercept of 2x+4y=12
(6,0)
100
Is this direct variation or partial variation?
Partial Variation
100
Determine the equation of a horizontal line passing through (5,3)
y=3
100
What are the three types of transformations?
Reflections, vertical stretches/compression, shifting up and down.
200
In the following word problem, identify the rate of change:
A streaming service costs $20 to sign up and $12 per month.
12
200
Find the y-intercept of 15x+12y=30
(0,2.5)
200
Is this direct or partial variation: y=4x
Direct Variation
200
What is the equation of a line with slope 1/2 and
y-intercept (0,12)
y=1/2x+12
200
How are you able to tell if there has been a reflection based on the equation of the line?
If the slope is negative.
300
In the following inequality, would you shade above or below the line? 2x+5<y
Above
300
Rewrite in Slope y-intercept form: 4x-2y=14
y=2x-7
300
Explain how you can determine if two lines are perpendicular from the equation?
If the slopes are negative recipricals of each other.
300
Is this line increasing or decreasing? y=-2x+5. How do you know?
Decreasing, the slope is negative.
300
Describe the transformations of the following line: y=2x-8
Vertical stretch (by a factor of 2)
Shift down 8 units.
400
In the following inequality would you use a solid or dotted line? y<3/4x-12
Dotted
400
Identify the x and y-intercepts of this line.
y-intercept (0,4)
x-intercept (-2,0)
400
Explain the difference between continuous and discrete data?
Continuous Data- both variables have the ability to have decimals and fractions.
Discrete Data- at least one variable cannot be a fraction or decimal.
400
Determine the point of intersection of the following two lines:
y=x+1
y=-x+5
(2,3)
400
Describe the transformations to the following line: y=-1/2x +2
Reflection across x axis
Vertical Compression (by a factor of 1/2)
Shift up 2 units.
500
A line has a slope of 4 and passes through the point (2,-1), find the equation of the line in slope-y-intercept form.
y=4x-9
500
What is the x-intercept of the line x=2?
What about the y-intercept?
(2,0)
There is no y-intercept
500
A school bus company charges $300 to rent the bus for the day plus an additional charge per student. Is this continuous or discrete data and why?
Discrete data because you cannot have a decimal of a student.
500
Determine the equation of a line that passes through (1,2) and (5,10)
y=2x
500
What direction does the line shift (clockwise or counterclockwise) if there is a vertical stretch?
Counterclockwise.