Question

test #4 geometry prep
name: nathan benite
first of year
form a date period
(1) which order - pair is shown on the coordinate plane? (g2a)
(2) a system of inequalities is graphed below.
which of the ordered pairs is in the shaded region? (g2a)
(3) jared graphed y = 2x+3 on a coordinate plane. how would the graph change if the 3 in the equation is changed to a 7? (g2b)

Explanation:

1. For the first question about the ordered - pair shown on the coordinate plane:

• # Explanation:
• ## Step1: Identify the point on the coordinate - plane
• Locate the point on the given grid. The \(x\) - coordinate is the horizontal position and the \(y\) - coordinate is the vertical position.
• ## Step2: Determine the coordinates
• Read the \(x\) and \(y\) values of the point.
• # Answer:
• Without seeing the actual point on the grid in your source (Edulastic), you would find the \(x\) and \(y\) values of the point. For example, if the point is 3 units to the right of the origin and 2 units up, the ordered - pair is \((3,2)\).

1. For the second question about the ordered pair in the shaded region of the system of inequalities:

• # Explanation:
• ## Step1: Recall the concept of inequalities and regions
• An ordered pair \((x,y)\) is in the shaded region if it satisfies all the inequalities in the system.
• ## Step2: Test the ordered pairs
• Substitute the \(x\) and \(y\) values of each ordered pair into the inequalities of the system and check if the inequalities are true.
• # Answer:
• Without the actual inequalities and ordered pairs from Edulastic, assume the inequalities are \(y\geq x\) and \(y\leq - x + 4\). If we have an ordered pair \((1,2)\), substituting into \(y\geq x\) gives \(2\geq1\) (true) and into \(y\leq - x + 4\) gives \(2\leq - 1+4=3\) (true), so \((1,2)\) is in the shaded region.

1. For the third question about the change in the graph of \(y = 2x+3\) when the equation is changed:

• # Explanation:
• ## Step1: Analyze the original equation
• The equation \(y = 2x + 3\) is in slope - intercept form \(y=mx + b\), where \(m = 2\) (slope) and \(b = 3\) (y - intercept).
• ## Step2: Analyze the new equation
• When the equation is changed, for example, if it becomes \(y = 2x+7\), the slope remains the same (\(m = 2\)), but the y - intercept changes from \(b = 3\) to \(b = 7\).
• ## Step3: Determine the graph change
• The graph of the line will shift vertically. If \(b\) increases, the line shifts up; if \(b\) decreases, the line shifts down.
• # Answer:
• If the equation changes from \(y = 2x + 3\) to \(y=2x + 7\), the graph of the line \(y = 2x+3\) will shift 4 units up because \(7-3 = 4\).

Answer:

1. For the first question about the ordered - pair shown on the coordinate plane:

• # Explanation:
• ## Step1: Identify the point on the coordinate - plane
• Locate the point on the given grid. The \(x\) - coordinate is the horizontal position and the \(y\) - coordinate is the vertical position.
• ## Step2: Determine the coordinates
• Read the \(x\) and \(y\) values of the point.
• # Answer:
• Without seeing the actual point on the grid in your source (Edulastic), you would find the \(x\) and \(y\) values of the point. For example, if the point is 3 units to the right of the origin and 2 units up, the ordered - pair is \((3,2)\).

1. For the second question about the ordered pair in the shaded region of the system of inequalities:

• # Explanation:
• ## Step1: Recall the concept of inequalities and regions
• An ordered pair \((x,y)\) is in the shaded region if it satisfies all the inequalities in the system.
• ## Step2: Test the ordered pairs
• Substitute the \(x\) and \(y\) values of each ordered pair into the inequalities of the system and check if the inequalities are true.
• # Answer:
• Without the actual inequalities and ordered pairs from Edulastic, assume the inequalities are \(y\geq x\) and \(y\leq - x + 4\). If we have an ordered pair \((1,2)\), substituting into \(y\geq x\) gives \(2\geq1\) (true) and into \(y\leq - x + 4\) gives \(2\leq - 1+4=3\) (true), so \((1,2)\) is in the shaded region.

1. For the third question about the change in the graph of \(y = 2x+3\) when the equation is changed:

• # Explanation:
• ## Step1: Analyze the original equation
• The equation \(y = 2x + 3\) is in slope - intercept form \(y=mx + b\), where \(m = 2\) (slope) and \(b = 3\) (y - intercept).
• ## Step2: Analyze the new equation
• When the equation is changed, for example, if it becomes \(y = 2x+7\), the slope remains the same (\(m = 2\)), but the y - intercept changes from \(b = 3\) to \(b = 7\).
• ## Step3: Determine the graph change
• The graph of the line will shift vertically. If \(b\) increases, the line shifts up; if \(b\) decreases, the line shifts down.
• # Answer:
• If the equation changes from \(y = 2x + 3\) to \(y=2x + 7\), the graph of the line \(y = 2x+3\) will shift 4 units up because \(7-3 = 4\).