Math Problem Statement

give me one example linear function solving with graphing with let x=0 4x-2

Solution

Let's solve the linear function 4x2=04x - 2 = 0 by graphing.

Step 1: Rearrange the equation

The equation of the line can be written as: 4x2=04x - 2 = 0 Simplify it: 4x=24x = 2 Divide both sides by 4: x=24=0.5x = \frac{2}{4} = 0.5

So, the solution is x=0.5x = 0.5.

Step 2: Graph the equation y=4x2y = 4x - 2

  1. Find the y-intercept (Let x=0x = 0): y=4(0)2=2y = 4(0) - 2 = -2 So, the y-intercept is (0,2)(0, -2).

  2. Find another point (Let x=1x = 1): y=4(1)2=2y = 4(1) - 2 = 2 So, the point (1,2)(1, 2) is on the line.

Step 3: Plot the points and draw the line

  • Plot the points (0,2)(0, -2) and (1,2)(1, 2).
  • Draw a straight line through these points.

The graph should show the line passing through x=0.5x = 0.5, which is where y=0y = 0. This confirms that the solution to the equation 4x2=04x - 2 = 0 is x=0.5x = 0.5.


Do you have any questions about this?

Related Questions:

  1. How do you determine the slope of a linear function from an equation?
  2. What is the significance of the y-intercept in a linear equation?
  3. Can you explain how to solve a linear equation algebraically?
  4. How do you find the x-intercept of a linear equation?
  5. What are the steps to graph a linear equation if given in slope-intercept form?

Tip: When graphing a linear equation, always start by plotting the y-intercept and then use the slope to find other points.

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Math Problem Analysis

Mathematical Concepts

Algebra
Linear Functions
Graphing Equations

Formulas

y = 4x - 2
Slope-intercept form y = mx + b

Theorems

Linear equation solving
Graphing linear functions

Suitable Grade Level

Grades 6-8