Math Problem Statement

Graph the equation: y - 4 = -2(x - 1).

Solution

The given equation is:

y4=2(x1)y - 4 = -2(x - 1)

Let's rewrite this equation into slope-intercept form y=mx+by = mx + b, where mm is the slope and bb is the y-intercept.

  1. Distribute the 2-2 on the right-hand side:

y4=2x+2y - 4 = -2x + 2

  1. Add 4 to both sides to isolate yy:

y=2x+6y = -2x + 6

Now the equation is in slope-intercept form: y=2x+6y = -2x + 6.

Graphing:

  • The slope m=2m = -2, meaning the line decreases by 2 units in yy for every 1 unit increase in xx.
  • The y-intercept b=6b = 6, which means the line crosses the y-axis at (0,6)(0, 6).

Steps for graphing:

  1. Plot the y-intercept at (0,6)(0, 6).
  2. Use the slope 2-2 (which can be written as 21\frac{-2}{1}) to move down 2 units in yy and 1 unit to the right in xx.
  3. Draw the line through these points.

Would you like further clarification or details on how to graph this? Here are five related questions you might consider:

  1. How do you calculate the slope between two points?
  2. How does changing the slope affect the graph of a line?
  3. What happens when you change the y-intercept in a linear equation?
  4. How do you find the equation of a line given two points?
  5. How can you check if a point lies on a given line?

Tip: When graphing a linear equation, always check the slope direction (positive/negative) to ensure the line tilts correctly!

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Math Problem Analysis

Mathematical Concepts

Linear Equations
Slope-Intercept Form

Formulas

y = mx + b (Slope-Intercept Form)

Theorems

Equation of a Line

Suitable Grade Level

Grades 8-10