Math Problem Statement

Graph the following line by plotting the intercepts and connecting them with a line. Your final graph should contain a line and two dots.

-2x-5y = 10

Solution

Here is the graph of the line 2x5y=10-2x - 5y = 10 using the intercepts. The points (5,0)(-5, 0) and (0,2)(0, -2) are plotted as dots, and the line passes through these points.

Do you want further details or have any questions?

Here are five related questions to deepen understanding:

  1. How would the graph change if the equation were 2x+5y=102x + 5y = 10?
  2. What would the slope of this line be?
  3. How can we find the intercepts for lines in standard form more efficiently?
  4. How do we graph lines that don’t have integer intercepts?
  5. What is the significance of intercepts in real-world applications?

Tip: When dealing with linear equations in standard form Ax+By=CAx + By = C, setting one variable to zero quickly finds the intercepts, making it easier to plot the line.

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Math Problem Analysis

Mathematical Concepts

Algebra
Linear Equations
Graphing

Formulas

Standard form of a line Ax + By = C
Intercepts: x-intercept (set y=0), y-intercept (set x=0)

Theorems

Intercepts method for graphing linear equations

Suitable Grade Level

Grades 8-10