Math Problem Statement

Find the intercepts. Then graph by using the intercepts, if possible. 2y-x=4

Solution

Step 1: Find the intercepts

To find the x-intercept, set y=0y = 0 and solve for xx: 2(0)x=4    x=4    x=42(0) - x = 4 \implies -x = 4 \implies x = -4 So, the x-intercept is (4,0)(-4, 0).

To find the y-intercept, set x=0x = 0 and solve for yy: 2y0=4    2y=4    y=22y - 0 = 4 \implies 2y = 4 \implies y = 2 So, the y-intercept is (0,2)(0, 2).

Step 2: Graph using the intercepts

Using the intercepts (4,0)(-4, 0) and (0,2)(0, 2), you can plot the line. These two points are enough to determine the straight line.

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If you have any questions, feel free to ask! Here are some related questions:

  1. How do you find the slope of the line from the equation?
  2. How do you rewrite the equation in slope-intercept form?
  3. What are the general steps to graph any linear equation?
  4. How do you find intercepts in nonlinear equations?
  5. Can you find the intercepts of a quadratic function?

Tip: The slope of a line can be calculated by using the formula y2y1x2x1\frac{y_2 - y_1}{x_2 - x_1}, which is useful when graphing based on points.

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Math Problem Analysis

Mathematical Concepts

Algebra
Linear Equations
Graphing

Formulas

Finding x and y intercepts
Standard form of a linear equation Ax + By = C

Theorems

Intercept theorem for linear equations

Suitable Grade Level

Grades 8-10