Math  /  Geometry

Questiony=2x+3y=-2 x+3
Step 2 of 2 : Plot the resulting set of ordered pairs using your answers from Step 1.
Answer (are plot one of the ordered pairs on the graph. Then, drag the other dot at the origin to plot the other ordered pair. by dragging or using the arrow keys. Enable Zoom/Pan

Studdy Solution

STEP 1

1. The equation of the line is y=2x+3 y = -2x + 3 .
2. We need to find ordered pairs (x,y)(x, y) that satisfy this equation.
3. We will plot these ordered pairs on a Cartesian coordinate system.

STEP 2

1. Calculate ordered pairs (x,y)(x, y) by choosing different values for x x and finding the corresponding y y .
2. Plot the ordered pairs on the Cartesian coordinate system.

STEP 3

Choose values for x x and calculate the corresponding values for y y using the equation y=2x+3 y = -2x + 3 .
Let's select x=0 x = 0 , x=1 x = 1 , and x=1 x = -1 :
\begin{align*} \text{For } x = 0, & \quad y = -2(0) + 3 = 3 \quad \Rightarrow \quad (0, 3) \\ \text{For } x = 1, & \quad y = -2(1) + 3 = 1 \quad \Rightarrow \quad (1, 1) \\ \text{For } x = -1, & \quad y = -2(-1) + 3 = 5 \quad \Rightarrow \quad (-1, 5) \\ \end{align*}

STEP 4

Plot the points (0,3)(0, 3), (1,1)(1, 1), and (1,5)(-1, 5) on the Cartesian coordinate system.
1. Plot the point (0,3)(0, 3) by starting at the origin (0,0)(0,0), moving 0 units along the x-axis and 3 units up the y-axis.
2. Plot the point (1,1)(1, 1) by starting at the origin, moving 1 unit along the x-axis and 1 unit up the y-axis.
3. Plot the point (1,5)(-1, 5) by starting at the origin, moving 1 unit left along the x-axis and 5 units up the y-axis.

Solution: The three points plotted on the Cartesian coordinate system are (0,3)(0, 3), (1,1)(1, 1), and (1,5)(-1, 5). These points should lie on the line described by the equation y=2x+3 y = -2x + 3 .

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