Math Problem Statement

Answer the questions regarding the graph: What is the y-intercept, slope, and equation of the line in slope-intercept form?

Solution

Let's go through the graph to answer the questions.

  1. y-intercept: This is the point where the line crosses the y-axis. From the graph, the line crosses the y-axis at y=2y = 2.

  2. Slope: To calculate the slope mm, we use the formula: m=ΔyΔxm = \frac{{\Delta y}}{{\Delta x}} From the graph, two points on the line are (0,2)(0, 2) and (5,5)(5, 5). So: m=5250=35m = \frac{{5 - 2}}{{5 - 0}} = \frac{3}{5} Therefore, the slope is 35\frac{3}{5}.

  3. Equation of the line in slope-intercept form: The slope-intercept form of a line is: y=mx+by = mx + b where mm is the slope and bb is the y-intercept. With m=35m = \frac{3}{5} and b=2b = 2, the equation becomes: y=35x+2y = \frac{3}{5}x + 2

So the answers are:

  • y-intercept: 22
  • slope: 35\frac{3}{5}
  • equation of the line: y=35x+2y = \frac{3}{5}x + 2

Would you like more details on any part of this?

Here are 5 related questions to deepen your understanding:

  1. How do you find the y-intercept if the graph isn't provided but you're given the equation?
  2. What happens to the slope if the line is steeper or flatter?
  3. Can you explain what the slope of 0 means in the context of a graph?
  4. How would you find the x-intercept of the line from the given equation?
  5. How can you use the slope formula to check if three points are collinear?

Tip: When calculating slope from a graph, always double-check the rise and run between two distinct points on the line to avoid calculation mistakes.

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Math Problem Analysis

Mathematical Concepts

Algebra
Coordinate Geometry
Linear Equations

Formulas

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

Theorems

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Suitable Grade Level

Grades 8-10