Math Problem Statement

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

Solution

Let's analyze the image.

The task is to write the equation of the line in fully simplified slope-intercept form. The slope-intercept form of a line is:

y=mx+by = mx + b

where:

  • mm is the slope of the line.
  • bb is the y-intercept (the value of yy when x=0x = 0).

Step 1: Identify two points on the line

Looking at the graph:

  • One point is (10,8)(-10, -8).
  • Another point is (0,4)(0, -4).

Step 2: Calculate the slope mm

The formula for slope between two points (x1,y1)(x_1, y_1) and (x2,y2)(x_2, y_2) is:

m=y2y1x2x1m = \frac{y_2 - y_1}{x_2 - x_1}

Using the points (10,8)(-10, -8) and (0,4)(0, -4): m=4(8)0(10)=4+810=410=25m = \frac{-4 - (-8)}{0 - (-10)} = \frac{-4 + 8}{10} = \frac{4}{10} = \frac{2}{5}

Step 3: Find the y-intercept bb

From the graph, the y-intercept is 4-4 (since the line crosses the y-axis at y=4y = -4).

Step 4: Write the equation

Now that we have the slope m=25m = \frac{2}{5} and the y-intercept b=4b = -4, the equation of the line in slope-intercept form is:

y=25x4y = \frac{2}{5}x - 4

This is the required equation.


Do you need further clarification or have any questions?

Here are 5 related questions:

  1. How do you convert between slope-intercept form and standard form?
  2. What does the slope represent in real-world applications?
  3. How can you determine if two lines are parallel or perpendicular?
  4. How do you find the x-intercept of a line from its equation?
  5. What happens to the graph of a line if the slope increases?

Tip: When finding the slope between two points, always pay attention to the signs to avoid calculation errors.

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Math Problem Analysis

Mathematical Concepts

Algebra
Linear Equations
Slope-Intercept Form

Formulas

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

Theorems

Slope-Intercept Form

Suitable Grade Level

Grades 8-10