Math Problem Statement

Write the equation of this line in slope-intercept form based on the graph provided.

Solution

To find the equation of this line in slope-intercept form, we need two main components:

  1. Slope (m)
  2. Y-intercept (b)

The slope-intercept form of a line is given by: y=mx+by = mx + b

Step 1: Determine the Slope (m)

The slope mm is calculated as: m=ΔyΔxm = \frac{{\Delta y}}{{\Delta x}} From the graph, let's choose two points on the line for clarity:

  • The point where x=0x = 0 and y=4y = 4 (the y-intercept)
  • Another point, such as where x=4x = 4 and y=0y = 0

Now, using these points: m=0440=44=1m = \frac{{0 - 4}}{{4 - 0}} = \frac{{-4}}{{4}} = -1

Step 2: Determine the Y-intercept (b)

From the graph, we observe that the line crosses the y-axis at y=4y = 4. Thus, the y-intercept bb is 4.

Final Equation

Substituting the values of mm and bb into the slope-intercept form: y=x+4y = -x + 4

Answer

The equation of the line in slope-intercept form is: y=x+4y = -x + 4

Would you like further clarification on any step?


Here are five related questions for deeper understanding:

  1. How would you calculate the equation if you were given two points not on the y-axis?
  2. What does a positive slope indicate about the direction of a line on a graph?
  3. How would the equation change if the y-intercept were negative?
  4. How can you verify if a given point lies on a specific line using its equation?
  5. What would be the equation of a line parallel to this one but passing through a different y-intercept?

Tip: To check if your slope calculation is correct, try picking different pairs of points on the line and see if you obtain the same slope.

Ask a new question for Free

By Image

Drop file here or Click Here to upload

Math Problem Analysis

Mathematical Concepts

Algebra
Linear Equations
Graphing

Formulas

Slope-intercept form y = mx + b
Slope formula m = (y2 - y1) / (x2 - x1)

Theorems

Slope-intercept form theorem

Suitable Grade Level

Grades 8-10