Math Problem Statement

Graph the equation y - 2 = -3(x - 1).

Solution

The equation you need to graph is:

y2=3(x1)y - 2 = -3(x - 1)

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

Step 1: Simplify the given equation

Start with: y2=3(x1)y - 2 = -3(x - 1) Distribute the 3-3 on the right-hand side: y2=3x+3y - 2 = -3x + 3 Now, add 2 to both sides to isolate yy: y=3x+5y = -3x + 5

Step 2: Identify the slope and y-intercept

  • Slope (mm): 3-3
  • y-intercept (bb): 5

Step 3: Plot the graph

  • The y-intercept is the point where the line crosses the y-axis, at (0,5)(0, 5).
  • The slope tells you that for every 1 unit increase in xx, yy decreases by 3 units (since the slope is negative).

Step 4: Draw points

  • Start at (0,5)(0, 5) for the y-intercept.
  • From (0,5)(0, 5), move 1 unit to the right (positive xx-direction), and 3 units down (negative yy-direction). This gives the point (1,2)(1, 2).
  • 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:

  1. How do you convert other forms of equations into slope-intercept form?
  2. What is the significance of the slope in linear equations?
  3. How do you find the x-intercept of a line from an equation?
  4. What happens when the slope is zero or undefined?
  5. 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.

Ask a new question for Free

By Image

Drop file here or Click Here to upload

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