Math Problem Statement

Write the equation of this line in slope-intercept form.

Solution

To find the equation of the line in slope-intercept form (y=mx+by = mx + b), we need two key pieces of information:

  1. The slope (mm): This is the "rise over run," or the change in yy over the change in xx.
  2. The y-intercept (bb): This is the point where the line crosses the yy-axis.

Step 1: Find the slope mm

Looking at the graph, the line passes through the points (0,16)(0, 16) and (4,4)(4, -4).

Using the slope formula: m=y2y1x2x1m = \frac{y_2 - y_1}{x_2 - x_1} Substituting the points (0,16)(0, 16) and (4,4)(4, -4): m=41640=204=5m = \frac{-4 - 16}{4 - 0} = \frac{-20}{4} = -5 So, the slope m=5m = -5.

Step 2: Find the y-intercept bb

The y-intercept is the value of yy when x=0x = 0. From the graph, we can see that the line crosses the yy-axis at 1616. Therefore, b=16b = 16.

Step 3: Write the equation

Now that we have the slope and the y-intercept, the equation of the line is: y=5x+16y = -5x + 16

This is the equation of the line in slope-intercept form.

Would you like any further details or explanations?

Here are 5 questions that expand on this concept:

  1. How do you calculate the slope when given two points on a line?
  2. What is the meaning of the slope and y-intercept in real-world problems?
  3. How does the slope affect the direction of a line on a graph?
  4. How would the equation change if the line had a positive slope?
  5. Can you determine the equation of a vertical or horizontal line?

Tip: The steeper the line, the larger the absolute value of the slope!

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Math Problem Analysis

Mathematical Concepts

Algebra
Linear Equations
Graphing

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