Math Problem Statement

Graph the equation y = -2x.

Solution

The equation given is y=2xy = -2x, which is a linear equation with a slope of -2 and a y-intercept of 0. This means that the graph is a straight line passing through the origin (0, 0), and the slope tells us that for every 1 unit increase in xx, yy decreases by 2 units.

Here’s how to plot the line on the graph:

  1. Start at the origin (0, 0), since there is no y-intercept term (i.e., the constant term is 0).
  2. Use the slope to find the next point. The slope 2-2 can be interpreted as "down 2 units for every 1 unit to the right." So from (0, 0), move 1 unit to the right (to x=1x = 1) and then 2 units down (to y=2y = -2). This gives the point (1, -2).
  3. You can also move to the left. From the origin, move 1 unit to the left (to x=1x = -1) and then 2 units up (to y=2y = 2). This gives the point (-1, 2).
  4. Draw a straight line through these points.

The line should pass through points such as (0, 0), (1, -2), and (-1, 2), and continue following the pattern established by the slope.

Would you like more details on how the slope affects the line or have any further questions?

Related questions:

  1. How do you find the slope of a line given two points?
  2. How would the graph change if the equation was y=2xy = 2x instead?
  3. What happens to the graph if you add a y-intercept, such as y=2x+3y = -2x + 3?
  4. How do negative slopes affect the direction of a line compared to positive slopes?
  5. Can you explain how to calculate the x-intercept of a linear equation?

Tip: The y-intercept is where the line crosses the y-axis, and the x-intercept is where the line crosses the x-axis. For y=2xy = -2x, the y-intercept is at (0, 0).

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Math Problem Analysis

Mathematical Concepts

Linear Equations
Slope-Intercept Form
Graphing

Formulas

Slope-intercept form: y = mx + b

Theorems

Slope theorem: Slope determines the steepness and direction of a line.

Suitable Grade Level

Grades 8-10