Math / Geometry

QuestionFor the system of equations below, graph each line to determine the solution. Write the solution as an ordered pair.
Each line must be drawn correctly and the solution must be correct in order to receive all points. $\left\{\begin{array}{l} y=\frac{2}{3} x+4 \\ y=-2 x-4 \end{array}\right.$
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Studdy Solution

STEP 1

1. The system consists of two linear equations.
2. The solution to the system is the point where the two lines intersect.
3. The equations are given in slope-intercept form, $y = mx + b$ .

STEP 2

1. Identify the slope and y-intercept for each line.
2. Graph the first line using its slope and y-intercept.
3. Graph the second line using its slope and y-intercept.
4. Determine the point of intersection.
5. Write the solution as an ordered pair.

STEP 3

Identify the slope and y-intercept for each line.
For the first equation $y = \frac{2}{3}x + 4$ : - Slope ( $m_1$ ) = $\frac{2}{3}$ - Y-intercept ( $b_1$ ) = 4
For the second equation $y = -2x - 4$ : - Slope ( $m_2$ ) = -2 - Y-intercept ( $b_2$ ) = -4

STEP 4

Graph the first line using its slope and y-intercept.
1. Plot the y-intercept (0, 4) on the graph.
2. Use the slope $\frac{2}{3}$ to find another point. From (0, 4), move up 2 units and right 3 units to reach (3, 6).
3. Draw the line through these points.

STEP 5

Graph the second line using its slope and y-intercept.
1. Plot the y-intercept (0, -4) on the graph.
2. Use the slope $-2$ to find another point. From (0, -4), move down 2 units and right 1 unit to reach (1, -6).
3. Draw the line through these points.

STEP 6

Determine the point of intersection.
1. Observe where the two lines intersect on the graph.
2. The intersection point is the solution to the system of equations.

STEP 7

Write the solution as an ordered pair.
The lines intersect at the point $(-3, 2)$ .
The solution to the system of equations is:
$\boxed{(-3, 2)}$

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Studdy Solution

STEP 1

1. The system consists of two linear equations.
2. The solution to the system is the point where the two lines intersect.
3. The equations are given in slope-intercept form, $y = mx + b$ .

STEP 2

1. Identify the slope and y-intercept for each line.
2. Graph the first line using its slope and y-intercept.
3. Graph the second line using its slope and y-intercept.
4. Determine the point of intersection.
5. Write the solution as an ordered pair.

STEP 3

Identify the slope and y-intercept for each line.
For the first equation $y = \frac{2}{3}x + 4$ : - Slope ( $m_1$ ) = $\frac{2}{3}$ - Y-intercept ( $b_1$ ) = 4
For the second equation $y = -2x - 4$ : - Slope ( $m_2$ ) = -2 - Y-intercept ( $b_2$ ) = -4

STEP 4

Graph the first line using its slope and y-intercept.
1. Plot the y-intercept (0, 4) on the graph.
2. Use the slope $\frac{2}{3}$ to find another point. From (0, 4), move up 2 units and right 3 units to reach (3, 6).
3. Draw the line through these points.

STEP 5

Graph the second line using its slope and y-intercept.
1. Plot the y-intercept (0, -4) on the graph.
2. Use the slope $-2$ to find another point. From (0, -4), move down 2 units and right 1 unit to reach (1, -6).
3. Draw the line through these points.

STEP 6

Determine the point of intersection.
1. Observe where the two lines intersect on the graph.
2. The intersection point is the solution to the system of equations.

STEP 7

Write the solution as an ordered pair.
The lines intersect at the point $(-3, 2)$ .
The solution to the system of equations is:
$\boxed{(-3, 2)}$

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Studdy Solution

STEP 1

1. The system consists of two linear equations.2. The solution to the system is the point where the two lines intersect.3. The equations are given in slope-intercept form, y=mx+b y = mx + b y=mx+b.

STEP 2

1. Identify the slope and y-intercept for each line.2. Graph the first line using its slope and y-intercept.3. Graph the second line using its slope and y-intercept.4. Determine the point of intersection.5. Write the solution as an ordered pair.

STEP 3

STEP 4

Graph the first line using its slope and y-intercept.1. Plot the y-intercept (0, 4) on the graph.2. Use the slope 23 \frac{2}{3} 32​ to find another point. From (0, 4), move up 2 units and right 3 units to reach (3, 6).3. Draw the line through these points.

STEP 5

Graph the second line using its slope and y-intercept.1. Plot the y-intercept (0, -4) on the graph.2. Use the slope −2-2−2 to find another point. From (0, -4), move down 2 units and right 1 unit to reach (1, -6).3. Draw the line through these points.

STEP 6

Determine the point of intersection.1. Observe where the two lines intersect on the graph.2. The intersection point is the solution to the system of equations.

STEP 7

Write the solution as an ordered pair.The lines intersect at the point (−3,2)(-3, 2)(−3,2).The solution to the system of equations is:(−3,2) \boxed{(-3, 2)} (−3,2)​

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Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

1. The system consists of two linear equations.
2. The solution to the system is the point where the two lines intersect.
3. The equations are given in slope-intercept form, $y = mx + b$ .

1. Identify the slope and y-intercept for each line.
2. Graph the first line using its slope and y-intercept.
3. Graph the second line using its slope and y-intercept.
4. Determine the point of intersection.
5. Write the solution as an ordered pair.

Graph the first line using its slope and y-intercept.
1. Plot the y-intercept (0, 4) on the graph.
2. Use the slope $\frac{2}{3}$ to find another point. From (0, 4), move up 2 units and right 3 units to reach (3, 6).
3. Draw the line through these points.

Graph the second line using its slope and y-intercept.
1. Plot the y-intercept (0, -4) on the graph.
2. Use the slope $-2$ to find another point. From (0, -4), move down 2 units and right 1 unit to reach (1, -6).
3. Draw the line through these points.

Determine the point of intersection.
1. Observe where the two lines intersect on the graph.
2. The intersection point is the solution to the system of equations.

Write the solution as an ordered pair.
The lines intersect at the point $(-3, 2)$ .
The solution to the system of equations is:
$\boxed{(-3, 2)}$