Math Problem Statement

Find the values of m and b for the line shown on the graph.

Solution

The image shows a straight line on a graph, and the question asks to find the values of mm (the slope) and bb (the y-intercept) of the line. Here's how we can solve this:

  1. Find the slope mm: The slope of a line is calculated using the formula: m=y2y1x2x1m = \frac{y_2 - y_1}{x_2 - x_1} We need two points on the line. From the graph, we can identify:

    • Point 1: (0,10)(0, 10) (the y-intercept)
    • Point 2: (2,6)(2, 6)

    Using these points: m=61020=42=2m = \frac{6 - 10}{2 - 0} = \frac{-4}{2} = -2

  2. Find the y-intercept bb: The y-intercept is where the line crosses the y-axis. From the graph, it's clear the line crosses at (0,10)(0, 10), so b=10b = 10.

Thus, the values of mm and bb are: m=2,b=10m = -2, \quad b = 10

Would you like more details or have any questions about these calculations?

Here are 5 related questions you can explore:

  1. How do you find the slope of a line if given different points?
  2. What happens to a line if the slope is positive vs. negative?
  3. Can you explain the relationship between the slope and the steepness of a line?
  4. How do parallel and perpendicular slopes relate to each other?
  5. How can the equation of a line change if shifted up or down on the y-axis?

Tip: When identifying the slope, always choose two points that are easy to read from the graph to avoid mistakes in calculations.

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Math Problem Analysis

Mathematical Concepts

Linear Algebra
Slope-Intercept Form

Formulas

m = (y2 - y1) / (x2 - x1)
y = mx + b

Theorems

Slope Formula
Y-Intercept in Linear Equations

Suitable Grade Level

Grades 8-10