7.11: Proficiency Exam
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Proficiency Exam
For the following problems, construct a coordinate system and graph the inequality.
−6x+4>−14
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x<3
−8<x+6≤−4
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−14<x≤−10
Plot the ordered pairs (3,1),(−2,4),(0,5),(−2,−2).
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As accurately as possible, label the coordinates of the points that have been plotted on the graph.
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(0,1),(3,3),(−3,0),(2,−3)
What is the geometric structure of the graph of all the solutions to the equation 2y+3x=−4?
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straight line
In what form is the linear equation in two variables ax+by=c?
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general form
In what form is the linear equation in two variables y=mx+b?
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slope-intercept
If an ordered pair is a solution to a linear equation in two variables, where does it lie geometrically?
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It lies on the line.
Consider the graph of y=27x+16. If we were to place our pencil at any point on the line and then move it horizontally 7 units to the right, how many units and in what direction would we have to move our pencil to get back on the line?
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2 units up
For the following problems, find the slope, if it exists, of the line containing the following points.
(−6, −1) and (0, 8)
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32
(−2, −8) and (−2, 10)
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no slope; vertical line at x=−2
Determine the slope and y−intercept of the line 3y+2x+1=0.
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slope = −23, y-intercept is (0,−13)
As we look at a graph left to right, do lines with a positive slope rise or decline?
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rise
For the following problems, find the equation of the line using the information provided. Write the equation in slope-intercept form
Slope = 4, y-intercept = −3.
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y=4x−3
Slope = −32, y-intercept = 43.
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y=−32x+43
Slope = 23, passes through (−1,2)
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y=23x+83
Slope = 7, passes through (0,0)
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y=7x
Passes through the points (5,2) and (2,1).
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y=13x+13
For the following problems, graph the equation of inequality.
y=13x−2
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y=13x−2
5y−2x+15=0
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4(x+y)=8
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4(x+y)=8
32y+2=0
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x=−2
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x=−2
2x+3y>6
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Reading only from the graph, determine the equation of the line.
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y=−13x+3