Math Problem Statement
Graph the equation: y - 4 = -2(x - 1).
Solution
The given equation is:
Let's rewrite this equation into slope-intercept form , where is the slope and is the y-intercept.
- Distribute the on the right-hand side:
- Add 4 to both sides to isolate :
Now the equation is in slope-intercept form: .
Graphing:
- The slope , meaning the line decreases by 2 units in for every 1 unit increase in .
- The y-intercept , which means the line crosses the y-axis at .
Steps for graphing:
- Plot the y-intercept at .
- Use the slope (which can be written as ) to move down 2 units in and 1 unit to the right in .
- 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:
- How do you calculate the slope between two points?
- How does changing the slope affect the graph of a line?
- What happens when you change the y-intercept in a linear equation?
- How do you find the equation of a line given two points?
- 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