Math Problem Statement

Write the equation of the line in fully simplified slope-intercept form.

Solution

To determine the equation of the line in slope-intercept form y=mx+by = mx + b, where mm is the slope and bb is the y-intercept, follow these steps:


Step 1: Find the Slope (mm)

The slope mm is calculated as: m=ΔyΔx=y2y1x2x1m = \frac{\Delta y}{\Delta x} = \frac{y_2 - y_1}{x_2 - x_1}

From the graph, identify two points on the line:

  • Point 1: (6,3)(-6, 3)
  • Point 2: (6,9)(6, 9)

Now substitute into the slope formula: m=936(6)=612=12m = \frac{9 - 3}{6 - (-6)} = \frac{6}{12} = \frac{1}{2}

The slope mm is 12\frac{1}{2}.


Step 2: Find the Y-Intercept (bb)

The y-intercept bb is the point where the line crosses the yy-axis. From the graph, the line crosses the yy-axis at (0,6)(0, 6).

Thus, b=6b = 6.


Step 3: Write the Equation

Substitute the slope m=12m = \frac{1}{2} and y-intercept b=6b = 6 into the slope-intercept form y=mx+by = mx + b: y=12x+6y = \frac{1}{2}x + 6


Final Answer:

The equation of the line in slope-intercept form is: y=12x+6y = \frac{1}{2}x + 6


Do you want me to explain how to verify the slope or graph the equation? Let me know if you have more questions!

Related Questions:

  1. How can you calculate the slope if only the graph is provided?
  2. What is the general form of a linear equation, and how does it relate to slope-intercept form?
  3. How do you determine the slope if the line passes through vertical or horizontal axes?
  4. Can you graph a line given its equation in slope-intercept form?
  5. How does changing the slope mm affect the steepness of the line?

Tip:

Always choose two clear points from a graph to calculate the slope accurately!

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Math Problem Analysis

Mathematical Concepts

Linear Equations
Slope-Intercept Form
Graphing Lines

Formulas

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

Theorems

The slope-intercept form theorem: A linear equation can be expressed as y = mx + b

Suitable Grade Level

Grades 8-10