Math Problem Statement
Graph the equation y - 2 = -3(x - 1).
Solution
The equation you need to graph is:
Let's first rewrite this equation in slope-intercept form, , where is the slope and is the y-intercept.
Step 1: Simplify the given equation
Start with: Distribute the on the right-hand side: Now, add 2 to both sides to isolate :
Step 2: Identify the slope and y-intercept
- Slope ():
- y-intercept (): 5
Step 3: Plot the graph
- The y-intercept is the point where the line crosses the y-axis, at .
- The slope tells you that for every 1 unit increase in , decreases by 3 units (since the slope is negative).
Step 4: Draw points
- Start at for the y-intercept.
- From , move 1 unit to the right (positive -direction), and 3 units down (negative -direction). This gives the point .
- Continue this pattern to find more points.
Once you plot these points, draw a straight line through them to represent the equation.
Would you like further assistance with the graph or more details?
Related Questions:
- How do you convert other forms of equations into slope-intercept form?
- What is the significance of the slope in linear equations?
- How do you find the x-intercept of a line from an equation?
- What happens when the slope is zero or undefined?
- How can you graph a line when given the slope and a single point?
Tip:
Always check the signs of the slope and y-intercept carefully when plotting.
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Math Problem Analysis
Mathematical Concepts
Linear equations
Slope-intercept form
Graphing
Formulas
y = mx + b (slope-intercept form)
Theorems
Slope of a line
Suitable Grade Level
Grades 7-10