Math Problem Statement

Two linear functions, y1 and y2, are graphed with their point of intersection indicated. Give the solution set of y1 = y2.

Solution

The problem asks to find the solution set of y1=y2y_1 = y_2 based on the intersection of two linear functions, y1y_1 and y2y_2, as shown on the graph.

From the image, we can observe that the two lines intersect at the point where:

  • x=10x = 10
  • y=19y = 19

Thus, the solution set for y1=y2y_1 = y_2 is the point where the two functions meet, which occurs at the coordinates (x,y)=(10,19)(x, y) = (10, 19).

Would you like further clarification on how the solution was derived?

Here are 5 related questions to consider:

  1. How can you find the intersection point of two linear equations algebraically?
  2. What does it mean for two functions to have an equal value at an intersection point?
  3. How can you verify the solution graphically and algebraically?
  4. How do slopes affect the point of intersection between two lines?
  5. What happens if two lines have the same slope but different y-intercepts?

Tip: In general, the intersection of two linear functions corresponds to solving the system of equations formed by the two lines.

Ask a new question for Free

By Image

Drop file here or Click Here to upload

Math Problem Analysis

Mathematical Concepts

Algebra
Linear Functions
Intersection of Lines

Formulas

y = mx + b (Equation of a Line)

Theorems

Intersection Point of Two Lines

Suitable Grade Level

Grades 8-10