Maintaining Mathematical Proficiency

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Exercises 1 In an (x,y) ordered pair, the first number shows the x-coordinate and the second number shows the y-coordinate.x-coordinate To graph (3,2), we first find 3 on the x-axis and make a mental note of this grid line. The x-coordinate "3" tells us to move three units in the positive horizontal direction.y-coordinate Next, we find 2 on the y-axis and follow this grid line until it collides with the grid line from our x-coordinate. The y-coordinate "2" tells us to move two units in the positive vertical direction.The point A(3,2) lies on the point at which these two grid lines intersect. We see that it is in Quadrant I.
Exercises 2 In an (x,y) ordered pair, the first number shows the x-coordinate and the second number shows the y-coordinate.x-coordinate To graph B(-5,1), we first find -5 on the x-axis and make a mental note of this grid line. The x-coordinate "-5" tells us to move five units in the negative horizontal direction.y-coordinate Next, we find 1 on the y-axis and follow this grid line until it collides with the grid line from our x-coordinate. The y-coordinate "1" tells us to move one unit in the positive vertical direction.The point B(-5,1) lies on the point at which these two grid lines intersect. We see that it is in Quadrant II.
Exercises 3 In an (x,y) ordered pair, the first number shows the x-coordinate and the second number shows the y-coordinate.x-coordinate To graph (0,3), we first find 0 on the x-axis and make a mental note of this grid line. The x-coordinate "0" tells us to not move in a horizontal direction.y-coordinate Next, we find 3 on the y-axis and follow this grid line until it collides with the grid line from our x-coordinate. The y-coordinate "3" tells us to move three units in the positive vertical direction.The point (0,3) lies on the point at which these two grid lines intersect. We see that it is on the positive y-axis.
Exercises 4 In an (x,y) ordered pair, the first number shows the x-coordinate and the second number shows the y-coordinate.x-coordinate To graph D(-1,-4), we first find -1 on the x-axis and make a mental note of this grid line. The x-coordinate "-1" tells us to move one unit in the negative horizontal direction.y-coordinate Next, we find -4 on the y-axis and follow this grid line until it collides with the grid line from our x-coordinate. The y-coordinate "-4" tells us to move four units in the negative vertical direction.The point D(-1,-4) lies on the point at which these two grid lines intersect. We see that it is in Quadrant III.
Exercises 5 In an (x,y) ordered pair, the first number shows the x-coordinate and the second number shows the y-coordinate.x-coordinate To graph (-3,0), we first find -3 on the x-axis and make a mental note of this grid line. The x-coordinate "-3" tells us to move three units in the negative horizontal direction.y-coordinate Next, we find 0 on the y-axis and follow this grid line until it collides with the grid line from our x-coordinate. The y-coordinate "0" tells us to not move in the vertical direction.The point E(-3,0) lies on the point at which these two grid lines intersect. We see that it is on the negative x-axis.
Exercises 6 In an (x,y) ordered pair, the first number shows the x-coordinate and the second number shows the y-coordinate.x-coordinate To graph (2,-1), we first find 2 on the x-axis and make a mental note of this grid line. The x-coordinate "2" tells us to move two units in the positive horizontal direction.y-coordinate Next, we find -1 on the y-axis and follow this grid line until it collides with the grid line from our x-coordinate. The y-coordinate "-1" tells us to move one unit in the negative vertical direction.The point F(2,-1) lies on the point at which these two grid lines intersect. We see that is in Quadrant IV.
Exercises 7 We are given an expression and asked to evaluate it when x=7. This means we should substitute x for 7 in the given expression and then simplify. 3x−4x=73(7)−4Multiply21−4Subtract term17 The expression evaluates to be 17.
Exercises 8 We are given an expression and asked to evaluate it when x=3. This means we should substitute x for 3 in the given expression and then simplify. -5x+8x=3-5(3)+8Multiply-15+8Add terms-7 The expression evaluates to be -7.
Exercises 9 We are given an expression and asked to evaluate it when x=5. This means we should substitute x for 5 in the given expression and then simplify. 10x+18x=510(5)+18Multiply50+18Add terms68 The expression evaluates to be 68.
Exercises 10 We are given an expression and asked to evaluate it when x=-4. This means we should substitute x for -4 in the given expression and then simplify. -9x−2x=-4-9(-4)−2-a(-b)=a⋅b36−2Subtract term34 The expression evaluates to be 34.
Exercises 11 We are given an expression and asked to evaluate it when x=-2. This means we should substitute x for -2 in the given expression and then simplify. 24−8xx=-224−8(-2)-a(-b)=a⋅b24+8⋅2Multiply24+16Add terms40 The expression evaluates to be 40.
Exercises 12 We are given an expression and asked to evaluate it when x=-1. This means we should substitute x for -1 in the given expression and then simplify. 15x+9x=-115(-1)+9a(-b)=-a⋅b-15+9Add terms-6 The expression evaluates to be -6.
Exercises 13 A coordinate plane has an x-axis and a y-axis. The intersection of these axes split the coordinate plane into four quadrants. One of each of the given points will lie in each quadrant. We will begin by plotting the first point.Plotting (a,b) It is given that a and b are both positive numbers. Thus, (a,b) will lie in the first quadrant, above the x-axis and to the right of the y-axis, the positive direction on both axes.Plotting (-a,b) Since a and b are both positive, -a will be negative. This means that the point (-a,b) will lie in the second quadrant. This is where x-values are negative and y-values are positive.Plotting (a,-b) Since a and b are both positive, -b will be negative. This means that the point (a,-b) will lie in the fourth quadrant. This is where x-values are positive and y-values are negative.Plotting (-a,-b) Since a and b are both positive, -a and -b will be negative. This means that the point (-a,-b) will lie in the third quadrant. This is where x- and y-values are negative.