While I can't create visual images directly, I can guide you on how to graph the line with a slope of -2/3 that passes through the point (0, 3).
Steps to Create the Graph:
-
Identify the Point: Start by marking the point (0, 3) on a coordinate plane. This point is on the y-axis.
-
Use the Slope: The slope of the line is -2/3. This means that for every 3 units you move to the right (positive x-direction), you move down 2 units (because the slope is negative).
-
Find Another Point:
- From (0, 3), move 3 units to the right (to x = 3).
- From that point, move down 2 units to (3, 1).
-
Plot the Second Point: Mark the point (3, 1) on your graph.
-
Draw the Line: Connect the points (0, 3) and (3, 1) with a straight line, extending in both directions.
-
Optional - Find More Points:
- If you want additional points, you can continue using the slope. From (3, 1), move another 3 units right and down 2: (6, -1). You can also do it in the opposite direction from (0, 3) going left to (-3, 5).
Equation of the Line:
If you want the equation of the line, you can use the point-slope form: \[ y - y_1 = m(x - x_1) \] where \( m \) is the slope and \( (x_1, y_1) \) is the point (0, 3).
Substituting in the values: \[ y - 3 = -\frac{2}{3}(x - 0) \]
Simplifying gives: \[ y = -\frac{2}{3}x + 3 \]
You can use this equation to plot additional points if needed.
Summary:
- Start at (0, 3)
- Move 3 units right and 2 units down to find (3, 1)
- Draw the line through these two points.
11 answers