Math Problem Statement

how to graph

Solution

Here's how to graph the line y=2x+3y = -2x + 3:

Step 1: Identify the slope and y-intercept

The equation is in slope-intercept form: y=mx+by = mx + b, where:

  • mm is the slope, and
  • bb is the y-intercept (the point where the line crosses the y-axis).

For y=2x+3y = -2x + 3:

  • The slope m=2m = -2,
  • The y-intercept b=3b = 3.

Step 2: Plot the y-intercept

The y-intercept is 33, so the line crosses the y-axis at the point (0,3)(0, 3). Start by plotting this point on the graph.

Step 3: Use the slope to find another point

The slope 2-2 means that for every 1 unit you move to the right on the x-axis, the line falls by 2 units on the y-axis. Starting from the point (0,3)(0, 3):

  • Move 1 unit to the right (to x=1x = 1),
  • Move 2 units down (to y=1y = 1).

Plot this second point at (1,1)(1, 1).

Step 4: Draw the line

Now that you have two points (0,3)(0, 3) and (1,1)(1, 1), draw a straight line passing through these points. This is the graph of the line y=2x+3y = -2x + 3.

Step 5: Extend the line

Continue the line in both directions (left and right) using the same slope. Make sure it extends across the graph, and label the points you used.


Example:

  1. Plot the point (0,3)(0, 3) on the graph.
  2. From (0,3)(0, 3), move right by 1 unit and down by 2 units to reach (1,1)(1, 1).
  3. Draw a straight line connecting these two points and extend it.

This will give you the graph of the line y=2x+3y = -2x + 3.

If you need more help or details, feel free to ask!


Related Questions:

  1. How do you determine the x-intercept of a line?
  2. What is the difference between positive and negative slopes in terms of graphing?
  3. How do you graph vertical and horizontal lines?
  4. How can you graph a line using two points instead of slope-intercept form?
  5. What are some strategies for accurately graphing lines without gridlines?

Tip:

When graphing, always start with the y-intercept, and then use the slope to find additional points. This helps ensure your line is accurate.

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Math Problem Analysis

Mathematical Concepts

Graphing
Linear Equations
Slope-Intercept Form

Formulas

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Theorems

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Suitable Grade Level

Grades 7-9