Math Problem Statement

Identify the slope and y-intercept of the line below (graph provided).

Solution

To determine the slope and y-intercept of the given line from the graph:

Step 1: Identify two points on the line

From the graph:

  • One point is (0,8)(0, 8) (y-intercept).
  • Another point is (2,6)(2, 6).

Step 2: Calculate the slope

The formula for slope is: m=y2y1x2x1m = \frac{y_2 - y_1}{x_2 - x_1} Substitute the points (0,8)(0, 8) and (2,6)(2, 6): m=6820=22=1m = \frac{6 - 8}{2 - 0} = \frac{-2}{2} = -1

So, the slope mm is 1-1.

Step 3: Determine the y-intercept

The y-intercept is the value of yy where the line crosses the y-axis. From the graph, the line crosses at y=8y = 8.

Final Answer:

  • Slope (mm): 1-1
  • Y-intercept (bb): 88

Would you like further clarification or additional examples?


Follow-up Questions:

  1. Can you calculate the slope using two other points from the graph?
  2. How would the equation of the line look using the slope-intercept form y=mx+by = mx + b?
  3. What does the negative slope tell you about the direction of the line?
  4. How can you verify the slope using the rise over run method directly from the graph?
  5. If the line extended, at what x-coordinate would y=0y = 0 (the x-intercept)?

Tip:

Always double-check the rise (change in yy) and run (change in xx) directly from the graph to ensure the slope is accurate.

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Math Problem Analysis

Mathematical Concepts

Slope and Y-intercept
Linear Equations
Graphing

Formulas

Slope formula: m = (y2 - y1) / (x2 - x1)

Theorems

Slope-Intercept Form: y = mx + b

Suitable Grade Level

Grades 6-8